EBER  C,   BYAM 

his  book 
Number          J 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

PRESENTED  BY 

PROF.  CHARLES  A.  KOFOID  AND 
MRS.  PRUDENCE  W.  KOFOID 


ECLECTIC   EDUCATIONAL    SERIES. 


THE  ELEMENTS 


OF 


NATURAL  PHILOSOPHY, 


SIDXEY  A.  NORTON,  A.M. 


Three  Hundred  and  J^'fty  Illustrations. 


VAX  ANTWERP,  BRAGG  &  CO., 

137    WALNUT  STREET,  28   BOND   STREET, 

CINCINNATI.  NEW  YORK. 


Entered  according  to  Act  of  Congress,  in  the  yoar  1870,  by 

WILSON,  IIINKLE  &  CO., 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for 
the  Southern  District  of  Oh'  :•. 


ECLECTIC    II 
VAN  AN 

CINCINNATI. 


PREFACE. 


THIS  work  is  the  result  of  many  years'  experience  in  teaching 
the  science  of  Physics.  In  its  preparation,  the  author  has  endeav- 
ored to  keep  constantly  in  mind  that  its  value  must  depend  on 
its  availability  as  a  text-book.  Accordingly  he  has  made  such  a 
selection  of  the  facts  and  principles  embraced  in  the  wide  range 
of  Natural  Philosophy  as,  in  his  judgment,  is  best  suited  to  the 
requirements  of  the  pupil. 

While  due  attention  has  been  given  to  the  recent  progress  in 
Physics,  including  the  latest  methods  and  inventions,  it  has  not 
been  forgotten  that  all  facts  are  equally  fresh  to  the  tyro,  al- 
though all  are  not  of  equal  importance,  as  regards  either  their 
fitness  for  developing  the  theory  of  the  science,  or  their  applica- 
tion to  the  practical  affairs  of  life.  For  this  reason,  nothing  has 
been  introduced  for  the  sake  of  its  novelty;  nor  have  cardinal 
principles  been  omitted,  because  a  former  generation  of  pupils 
has  studied  them. 

It  has  been  an  object  of  careful  thought  to  present  the  science, 
in  all  its  departments,  in  a  manner  at  once  systematic  and  sym- 
metrical. Of  course,  no  pretense  is  made  of  exhausting  the  sub- 
ject, but  it  is  hoped  that  the  student  will  find  in  this  treatise  all 
that  is  necessary  for  his  purposes.  While  fully  impressed  that 
"there  is  no  royal  road  to  science,"  the  author  has  yet  endeavored 


iv  PREFACE. 

to  make  the  labor  of  the  student  as  attractive  and  invigorating 
as  possible.  To  this  end,  the  subject  has  been  treated  not  merely 
as  a  science  to  be  learned,  but  also  as  a  means  of  educational  dis- 
cipline: the  topics  are  considered  in  their  logical  order,  method- 
ically developed,  thoroughly  illustrated  and  enforced. 

No  pains  have  been  spared  to  secure  clearness  of  expression, 
precision  in  definitions,  and  accuracy  in  the  statement  of  facts. 
The  manuscript  was  read  by  Prof.  Charles  H.  Smith,  the  proof 
sheets  by  Mr.  H.  H.  Vail,  and  to  these  gentlemen  the  author 
returns  his  sincere  thanks.  Should  any  errors  have  escaped  their 
notice,  the  author  will  thank  any  of  his  readers  who  will  have 
the  kindness  to  inform  the  publishers  of  such  as  he  may  find. 

The  problems  are  placed  in  the  appendix  for  greater  conven- 
ience. If  properly  used,  they  will  serve  not  only  to  test  the 
knowledge  acquired  by  the  student,  but  also  to  lead  him  to  think 
on  the  nature  of  the  laws  and  principles  required  for  their  correct 
solution. 


TABLE   OF  CONTENTS. 


CHAPTER  I.  PAOB 

INTRODUCTION, 7 

CHAPTER  II. 

SOMATOLOGY, 13 

The  Universal  Properties  of  Matter, 14 

The  Specific  Properties  of  Matter, 26 

Phenomena  connected  with  Adhesion, 38 

CHAPTER  III. 

THE  MECHANICS  OP  SOLIDS, 51 

General  Statics  and  Dynamics, 51 

Statics, 74 

Dynamics,           ...........  106 

CHAPTER  IV. 

THE  MECHANICS  OF  FLUIDS, 135 

Hydrostatics, 135 

Hydrodynamics, 160 

Pneumatics, 171 

,       CHAPTER  V. 

UNDULATIONS, 196 

CHAPTER  VI. 

ACOUSTICS, 212 

The  Nature  of  Sound, 214 

The  Theory  of  Music, 225 


yi  CONTENTS. 

CHAPTER  VII.  PAGE 

OPTICS, 238 

The  Reflection  of  Light, 247 

The  Refraction  of  Light, 257 

Colors, 268 

Vision  and  Optical  Instruments, 284 

Double  Refraction  and  Polarization, 297 

CHAPTER   VIII. 

PYRONOMICS, 305 

The  Effects  of  Heat, 305 

The  Distribution  of  Heat, 332 

The  Sources  of  Heat, 345 

The  Dynamical  Theory  of  Heat, 350 

The  Steam  Engine, 356 

CHAPTER  IX. 

ELECTRICITY, 364 

Magnetism, 364 

Statical  Electricity, 373 

Dynamical  Electricity, 391 

Electro-Magnetism, 422 

Electro-Dynamic  Induction, 436 

Magneto-Electricity, 437 

Thermo-Electricity, 441 

PROBLEMS, 445 

.j;»y 

NMII;.     The    following    t:il>l<i    lias  boon   prepared   for  the   Con- 
venience  of   -chools    in    which    the    time    allotted    to    the   study    of 

Natural    Philosophy  is  not  siiflieieiit   for  the  mastery  of  the  entire 

work.  Tin-  topics  indicated  till  about  ei-hty  paires.  The  omis- 
sion of  these  \\ill  irive  the  student  a  shorter  course,  which  is 
still  complete  in  it-elf. 

to  be  omitted  in  the  shorter  conr>e: 

817         18  -582   624  —  689 

7   378  —  380   587   ~'l<;   648   ^'^ 
286  —  312   419  —  487   <;"•>   610   us  1 —682 
747  —  759 


NATURAL  PHILOSOPHY. 


CHAPTER   I. 

INTRODUCTION. 

1.  Matter  is  any  thing  that  possesses  extension  and  im- 
penetrability ;  as  earth,  water,  air.     The  different  kinds  of 
matter  are  called  substances. 

2.  Force  is  that  which  causes  any  change  in  the  form  or 
condition  of  matter;    as  heat,  electricity.     We  know  very 
little  of  the  ultimate  nature  of  matter  and  force,  because  it 
is  difficult  to  conceive  of  either  alone.     All  the  phenomena 
of  the  visible   universe  are  caused  by  the  action  of  force 
upon  matter. 

3.  A  body   is   any  separate  portion  of  matter,   whether 
large  or  small ;    as  a  cannon,  a  cannon  ball.     Every  body 
is  considered   as  made   up  o£  very  small  particles,  called 
molecules,  each  of  which  is  supposed  to  contain  two  or  more 
still   smaller  particles,    called   atoms.     It   is   also   supposed 
that  these  atoms  do  not  touch  each  other,  but  are  retained 
side  by  side  by  means  of  certain  forces  known  as  molecular 
attraction*.     The  firmness  of  their  union  is  modified  by  the 
presence   of  an   opposing   force   called    molecular  repulsion. 
Heat  is   the  principal,  if  not  the  only,   repellant  force  in 
Nature. 

(7) 


8  NATURAL   PHILOSOPHY. 

4.  With  respect  to  the  coherence  of  its  molecules,  a  body 
is   said   to  be  in  one  of  three  states:    1.  solid;    2.  liquid; 
3.  aeriform,  or  gaseous. 

1 .  A  body  is  in  the  solid  state  when  the  relative  position 
of  its  molecules  can  not  be  changed  without  the  expenditure 
of  considerable  force;   as  ice,  marble,  iron.     Bodies  in  this 
state  are  called  vW /'»/>• ,  and  retain  whatever  shape  has  been 
given  them  by  nature  or  art. 

2.  A  body  is  in  the  liquid  state  when  the  relative  position 
of   its   molecules   is    easily   changed;    as    water,    oil,    wine. 
Bodies  in  this  state  are  called  Liquids,  and  assume  with 
readiness  the  shape  of  any  vessel  into  which  they  may  be 
poured. 

3.  A  body  is  in  the  aeriform   or  gaseous  state  when  its 
molecules  tend  to  separate  and  occupy  a  greater  volume ; 
as    steam,    air,    oxygen.     Bodies   in    this    state    are   called 

form  Bodies,  Gases,  or  Vapors. 

The  term  fluid  is  applied  to  both  liquid  and  aeriform  bodies:  as 
water,  steam.  The  same  substance  may,  at  different  times,  be  in 
either  of  these  three  states,  according  to  the  relations  which  c.\i-t 
between  the  molecular  attractions  and  repulsions.  Thus,  by  a  mod- 
erate chanire  in  the  temperature,  water  may  be  made  to  pass  through 
the  solid,  liquid,  and  aeriform  states;  as  ice,  water,  steam.  So,  also, 
many  metals  may  hi-  easily  niched,  and  then  changed  into  vapors. 

5.  The  number  of  distinct  substances  is  almost  infinite; 
but  every  body  consists,  either  (1.)  of  a  single  element,  or, 
(2.)    of  several  elements  combined.     With   respect   to  the 
nu  mix T  of  elements  it  contains,  a  body  is  said  to  be  either 
(1.;  simple  or  (2.)  compound. 

1.  A  simple  substance  contains  but  one  element;  as  iron, 

gold,  diamond. 

2.  A  compound  substance  contains  two  or  more  elements  ; 
as  water,  oil,  alum. 

Then-  arc  .-ixty--ix  elements  now  recn-jni/cd.  but  a  more  riiron.iis 
analysis  may  either  increase  or  diminish  this  number.  Very  few 
elements  are  found  native:  by  far  the  greater  number  are  derived 


FORCES.  9 

from  their  combinations.  Only  eighteen  or  twenty  may  be  obtained 
in  any  considerable  quantity.  The  rest  appear  to  play  a  subordinate 
part  in  the  structure  of  our  globe,  and  are  known  only  to  chemists. 

6.  Forces  are  either  Attractive  or  Repellent    according  as 
they  cause  the  particles  of  matter  (1.)  to  approach,  or,  (2.) 
to  recede  from  each  other.     Force  may  act  either  (1.)  only 
upon  the  molecules  of  matter  and  at  distances  which  are 
inappreciable  to  our  senses,  or,  (2.)  also  upon  bodies  taken 
as  a  whole,  and  at  any  distance,  whether  small  or  great. 
The  forces  of  the  first  class  are  called  the  Molecular  Forces, 
and  are  severally  named  (1.)  cohesion,  (2.)  adhesion,  (3.) 
affinity.     Those   of  the  second   class  are   (1.)    gravitation, 
(2.)  light,  (3.)  heat,  which  always  acts  as  a  repellant  force, 
(4.)  electricity,  which  is   both  an  attractive  and   repellent 
force. 

The  forces  of  affinity,  electricity,  heat,  and  light,  are  so  closely 
allied  that  many  philosophers  consider  them  as  modifications  of  the 
same  force,  in  the  same  sense  that  magnetism  is  a  modification  of 
electricity.  We  know  that  the  action  of  either  of  these  forces  may 
induce  the  action  of  any  other  of  them ;  thus  the  action  of  affinity 
may  induce  heat,  then  light,  as  is  shown  by  the  burning  of  a  candle. 
For  this  reason,  they  are  called  the  coirdative  forces.  Heat,  light,  and 
electricity  are  sometimes  termed  the  imponderable  agents,  from  an 
erroneous  notion  that  they  are  matter  without  weight. 

7.  All  these  are  the  forces  of  inanimate  nature.     Plants 
and  animals  live  and  move  by  virtue  of  higher  vital  forces, 
which    control   and  modify   all   other  forces   in  an   entirely 
inexplicable  manner. 

The  forces  already  named  are  the  only  ones  of  which  we  have  any 
knowledge.  They  produce,  by  their  action  on  matter,  secondary  forces, 
which  are  employed  by  man  in  machines.  Thus  the  molecular  forces 
give  strength  and  elasticity  to  springs.  Heat  develops  the  elastic 
force  of  steam,  and,  acting  in  conjunction  with  gravitation,  raises 
winds  which  cause  the  waves  of  the  seas.  Gravitation  is  made  serv- 
iceable to  man  in  the  force  of  running  water,  and  in  machinery 
moved  by  weights.  The  muscular  strength  of  men  and  animals  is 
the  result  of  many  forces,  as  heat,  cohesion,  affinity,  modified  by  the 
vital  forces. 


10  NATURAL   PI1ILOSOPHV. 

8.  The  changes  to  which  all  bodies  arc  liable  may  be 
reduced  to  two  classes:  (1.)  those  by  which  the  substance 
is  not  altered  so  a-  to  lose  its  identity,  and  (2.)  tho.M-  hy 
which  its  identity  is  entirely  lost.  Thus  (1.)  a  mu>s  of 
iron  may  be  hurled  from  a  cannon,  or  wrought  into  nails, 
or  beaten  into  a  plowshare,  or,  by  contact  with  a  magnet, 
become  endowed  with  the  property  of  attracting  iron  tilings, 
but,  notwithstanding  these  changes  of  position,  shape,  and 
size,  or  even  properties,  we  still  recognize  it  as  iron. 

So  water  may  be  converted  into  ice  or  steam  and  yet 
preserve  its  identity,  for  if  the  ice  be  melted  or  the  steam 
condensed,  the  fluid  water  re-appears  with  its  characteristic 
properties.  So,  also,  if  a  bit  of  hard  rubber  or  sealing-wax 
be  rubbed  with  a  silk  handkerchief,  it  will  become  endowed 
with  the  property  of  attracting  and  then  repelling  small 
pieces  of  paper  or  pith,  although  we  can  not  perceive  any 
change  in  the  structure  of  either.  Such  changes  are  called 
"/  changes.  The  agencies  by  which  they  are  pro- 
duced are  the  physical  forces,  of  which  the  principal  are 
gravitation,  cohesion,  and  the  secondary  forces. 

(2.)  On  the  other  hand,  if  the  iron  be  exposed  to  moist 

air  it  crumbles  to  a   red   powder;    if  it  be  placed  in  weak 

sulphuric   acid,    it   is   converted    into   a   green,    crystalline 

solid.     If   steam    he    pa— ed  over  red   hot  iron,  it  yields  a 

combustible   gas    (hydrogen).      If  sealing-wax   is  burned,  it 

away  into  colorless  gases  which   can   never  again   be 

united    tn    form    wax.       Such    changes    are    called    clu-miml 

0,  and    the    agencies   by  which    they  are   caused    art* 

called    rhnninil  forces.       The    principal    chemical    force    is 

affinity. 

Light,  heat,  and  electricity,  in  their  action  on  matter 
generally  product-  physical  changes,  but  they  sometimes 
a  —  i-t  in  producing  chemical  change,  or  they  are  evoked  by 
the  action  of  chemical  affinity:  thus,  if  \\e  heat  a  strip  of 
/ine,  it  increa-e-  in  >i/c,  then  melts,  and,  finally,  if  no  air 
i-  piv-«-nt,  panel  away  in  a  Mate  of  vapor:  but,  on  cooling, 
the  vapor  lir.-t  become.-  liquid,  then  solid,  and,  at  last,  con- 


PROPERTIES.  11 

tracts  to  its  original  dimensions,  showing  that  all  these 
change*  are  physical.  On  the  other  hand,  if  zinc  is  strongly 
heated  in  the  air,  it  burns  away  to  a  soft  and  bulky  pow- 
der sometimes  used  as  a  white  paint.  This  permanent 
change  is  due  to  chemical  affinity,  assisted  by  heat. 

9.  Two  classes   of  properties   correspond    to  these   two 
classes   of   changes.      (1.)    Those   which   a   substance    may 
exhibit   without  undergoing  any  change  itself,    or  causing 
any   essential    change    in    other  bodies,  are   called  physical 
properties.       (2.)    Those    which    relate    to    the    permanent 
change  which  a  substance  may  experience  itself,  or  effect  in 
other  substances,  are  called  chemical  properties :  thus,  among 
the  physical  properties  of  iodine  are  its  luster,  weight,  its 
purple  vapor,  etc.;    among   its   chemical  properties   are  its 
power  of  turning  starch  blue,  of  setting  fire  to  phosphorus, 
of  combining  with  other  elements,  etc. 

10.  The  changes,  forces,  and  properties  relating  to  matter 
may  thus  be   classified  in  two  distinct  groups.     The  study 
of  the  laws  and  phenomena  which  severally  relate  to  each 
group  has  given  rise  to  two  distinct  sciences,  (1.)  Natural 
Philosophy,  or  Physics,  and  (2.)  Chemistry. 

CHEMISTRY  considers  those  phenomena  in  which  the  sub- 
stances acted  upon  suffer  a  loss  of  identity. 

X  ATTIJAL  PHILOSOPHY,  or  PHYSICS,  considers  those  phe- 
nomena in  which  the  substances  acted  upon  do  not  suffer  a 
loss  of  identity. 

11.  The  laws  and  phenomena  which  belong  to  the  domain 
of  natural  philosophy  are   so  varied   and   numerous  that  it 
has    been    found    necessary    to    divide    them    into    several 
branches  of  study;    each   of  which   is  of  sufficient   impor- 
tance to  merit  the  name  of  a  distinct  science.     It  will  be 
found  convenient  to  make  an  arbitrary  division  of  Natural 
Philosophy  into  Physics  and  Chemical  Physics. 


12  NATURAL  PHILOSOPHY. 

12.  PHYSICS  considers  the  forces  whose  phenomena  are 
never  attended  by  chemical  changes.  It  includes  three 
branches  : 

(1.)  Somatology,  which  treats  of  the  properties  of  matter. 

(2.)  Mechanics,  which  treats  of  equilibrium  and  motion. 

(3.)  Acoustics,  which  treats  of  sound. 

CHEMICAL  PHYSICS  considers  the  forces  whose  phenomena 
are  sometimes  attended  by  chemical  changes.  It  also 
includes  three  branches: 

(1.)  Pyronomics,  which  treats  of  heat. 

(2.)  Optics,  which  treats  of  light. 

(3.)  Electricity,  which  treats  of  electrical  forces. 

Some  of  these  branches  are  again  subdivided,  as  will  be 
seen  hereafter.  The  mechanics  of  the  heavenly  bodies  con- 
stitutes the  science  of  astronomy. 

13.  Recapitulation. 

Bodies  are  classified  : 

{Solid;  as  ice. 
Liquid  ;  as  water. 
Aeriform;  as  steam. 

II.  With  regard  to  composition.      {  SimPle5  as  ox^en- 

^  Compound  ;  as  water. 

S<  it  nces  which  treat  of  the  action  of  force  upon  inanimate  matter 
are: 

t  Somatology. 
Physics.  \  Mechanics. 

Natural  Philosophy,  which  includes  1 


.^  f        onomcs. 

w.      °Ptics;  . 
v  Electricit. 


Phyriw.  . 

Electricity. 

Chemistry,  which  treats  of  Chemical  Affinity. 

Forces  in  their  action  upon  matter  are  either  attractive  or  repellant 

I. 

t  Cohesion. 

Act  only  on  molecules.  Molecular,  -j  Adlu-ion. 

(  Affinity. 


8OMATOLOOT. 


General. 


13 


Act  also  upon  bodies. 


(Electricity. 
Heat. 
Light. 


[  Universal. 

Gravitation. 

II. 

{Gravitation. 

Never  cause  loss  of 
identity. 

{  Physical. 

Cohesion. 
Adhesion. 

Sometimes  attend  loss 
of  identity. 

{  Chemico-Physical. 

{Light. 
Heat, 

Electricity. 

Always  cause  loss  of 
identity. 

{  Chemical. 

{  Affinity. 

CHAPTER    II. 


14.  By  studying  the  properties  of  iron,  it  is  found  that 
they  may  be  divided  into  two  classes  :  one  class  includes 
properties  which  it  possesses  in  common  with  all  other  sub- 
stances ;  the  other  class  includes  properties  which  are 
peculiar  to  iron,  and  which  distinguish  it  from  all  other 
kinds  of  matter. 

Thus,  (1.)  a  mass  of  iron  occupies  a  certain  portion  of 
space  to  the  exclusion  of  all  other  bodies  ;  that  is,  it  pos- 
sesses extension  and  impenetrability  ;  it  also  has  weight  : 
but  every  other  substance,  whether  solid,  liquid,  or  aeriform, 
possesses  extension,  impenetrability,  and  weight.  Properties 
which  belong  to  all  bodies  are  called  universal  properties. 

(2.)  Besides  these,  iron  is  endowed  with  other  properties 
peculiar  to  itself.  Thus,  iron  not  only  possesses  extension, 
but  has  a  peculiar  crystalline  form  ;  it  not  only  possesses 
weight,  but  every  piece  of  iron  weighs  7.8  times  as  much  as 
an  equal  bulk  of  water  ;  it  has  a  certain  hardness,  strength, 


11  NATURAL   PHILOSOPHY. 

flexibility,  and  a  familiar  luster.      Properties  which  are  pe- 
culiar to  a  substance,  and  serve  to  characterize  it,  are  called 


15.  The  Universal  Properties  of  matter  are  (1.)  exten- 
sion, (2.)  impenetrability,   (3.)  weight,   (4.)  mobility,   (5.) 
inertia,  (6.)  divisibility,  (7.)  porosity,  (8.)  compressibility, 
(9.)  expansibility,  (10.)  indestructibility,  (11.)  elasticity. 

The  first  two  of  these  may  be  termed  the  essential  prop- 
erties of  matter,  since  they  serve  to  define  it.  The  last  nine 
may  be  conceived  of  as  not  applying  to  atoms,  but  only  to 
bodies,  and  hence  may  be  termed  general  properties. 

The  most  important  Specific  Properties  are  (1.)  elas- 
ticity, (2.)  tenacity,  (3.)  hardness,  (4.)  brittleness,  (5.)  duc- 
tility, (6.)  malleability.  Besides  these  might  be  named 
others,  as  color,  transparency,  taste,  odor,  as  well  as  the 
relations  which  bodies  bear  to  heat,  sound,  and  electricity. 

THE    UNIVERSAL    PROPERTIES    OF    MATTER. 

16.  Extension   or   Magnitude   is  that  property  by  virtue 
of  which  a  body  occupies  a  certain  space. 

Extension  has  three  dimensions  —  length,  breadth,  and 
thickness.  No  one  can  conceive  of  a  body  which  does  not 
possess  all  these.  As  a  necessary  consequence,  every  body 
lias  a  certain  si  i  ape  or  figure.  The  figure  of  solids  is  per- 
manent; the  figure  of  fluids  varies  with  the  shape  of  the 
vessel  which  contains  them.  The  amount  of  .-pace  that  a 
body  occupies  is  termed  its  Volume  or  l>ulk. 

17.  For   the    purpose    of   measuring  length,    England   and 
the    I'liiteil    State-    have    adopted    an    arbitrary    unit    called 
the  Yard,  with  its  multiples  and  divisions,  rods,  inches,  etc. 
The    unit    adopted    by    France    is    the    metre,    which    is    the 
forty    millionth    part   of   a    meridian   of    our    globe,    and    is 
e'|ii;il  to  inches  used  in  the  V.  S.  coa-t  Mirvey. 

All  tin-  l-'ivjirh   measure   increase  .-mil  <UVIV;IM-  in  divinm!  pro- 

portion.      F<>r     lh<-     im-ivuM-,    the    (ireek    prefixes    drr.-i    'I";,    hecto 


WEIGHT. 


15 


(100),  and  kilo  (1000)  are  used:  for  the  de- 
crease, the  Latin  prefixes  deci  (TV),  centi 
(T^),  mille  (j^ny)  are  used.  A  decimetre  is 
drawn  on  the  margin  in  comparison  with  a 
scale  of  inches.  It  will  be  seen  that  one  inch 
is  a  trifle  longer  than  25  millimetres. 

The  units  of  surface  and  volume, 
derived  from  the  linear  unit,  are  called 
the  square  inch,  cubic  inch,  etc.  The 
wine  gallon  of  the  United  States  con- 
tains 231  cubic  inches.  The  English 
imperial  gallon  contains  277.274  cubic 
inches. 

The  French  unit  of  volume,  called  the 
litre,  is  a  cubic  decimetre,  containing  61.022 
cubic  inches  or  2.113  wine  pints. 

18.  Weight  is  due  to  the  force  of 
gravitation,  by  virtue  of  which  every 
particle  of  matter  attracts  every  other 
particle  toward  itself.  A  falling  body 
is  drawn  by  the  attraction  of  all  the 
particles  of  the  earth  toward  the  center 
of  the  globe ;  but,  when  the  body  is 
not  free  to  fall,  the  force  which  the 
earth's  attraction  exerts  upon  it  is 
expended  in  pressure  against  its  sup- 
port. This  pressure  is  called  absolute  weight.  Hence, 
weight  is  the  measure  of  the  earth's  attraction,  and  must 
vary  as  the  attraction  varies.  This  definition  limits  weight 
to  bodies  on  the  earth,  but,  as  the  attraction  of  gravitation 
is  universal,  a  body  would  possess  weight  if  removed  to 
any  of  the  heavenly  bodies. 

19.  The  unit  of  weight  adopted  by  the  United  States 
and  England  is  the  avoirdupois  pound,  of  7,000  grains. 

The  French  unit,  called  a  gramme,  is  the  weight  of  a 
cubic  centimetre  of  distilled  water  at  39°. 2  F.  A  gramme 


w  —  - 

0  = 

>J 

- 
05  = 

- 

c       t 

FIG.  1. 


16  NATURAL   PHILOSOPHY. 

equals  15.434  grains.     A  kilogramme  equals  15434  grains, 
or  2.2046  avoirdupois  pounds. 

'.  hi  ^Pounds,  of  one  Cubic  Foot  at  62°  F. 

Potassium 53. 

Wrought  Iron 480. 

Copper 556. 

Lead 712. 

Gold 1224. 

Platinum 1373. 


Hydrogen  0.005592 

Nitrogen  0.07841 

Air 0.080728 

Oxygen 0.089256 

Water 62.418 

Mercury  848.75 


20.  Impenetrability  is  that  property  by  virtue  of  which 
two  bodies  can  not  occupy  the  same  portion  of  space  at  the 
same  time. 

When  a  solid  is  immersed  in  a  fluid,  it  displaces  a  quantity  of  fluid 
equal  to  its  own  volume.  Thus,  if  a  pebble  be  dropped  into  a  tumbler 
full  of  water,  enough  water  will  overflow  to  equal  the  size  of  the 
pebble.  Even  a  needle  will  displace  its  own  bulk,  for,  although  no 
one  may  be  able  to  detect  any  change  of  level  on  the  addition  of  a 
single  needle,  if  many  needles  are  dropped  into  the  tumbler,  the  water 
will  overflow  as  before.  If  one  end  of  a  glass  tube  be  closed  by  the 
thumb,  and  the  other  end  plunged  into  a  vessel  of  water,  the  water 
can  not  enter  the  tube  because  of  the  impenetrability  of  the  air  en- 
closed in  the  tube;  but,  when  the  thumb  is  removed,  the  air  will  be 
expelled,  and  the  water  will  rise  to  the  level  of  that  in  the  vessel. 

21.  This  property  belongs  to  all  bodies,  solid,  liquid,  and 
gaseous,  though  there  are  some  apparent  exceptions. 

Thus,  in  the  last  example,  the  water  will  rise  a  little  way  in  the 
tube;  but  this  occurs  because  the  air  is  compressible.  A  nail  may  be 
driven  into  a  board  without  increasing  its  size,  but  this  is  effected  by 
separating  the  fibers  of  the  wood  and  crowding  them  together  to  make 
room  tor  the  harder  body.  If  a  long  and  slender  test  tube  be  half 
tilled  with  water,  and  strong  alcohol  be  poured  in  carefully  so  as  not 
to  mix  tin-  liquids  until  the  tube  is  quite  full,  and  then  the  liquids 
be  thoroughly  shaken  together,  the  mixture  will  no  longer  fill  the 
tube.  The  reason  for  this  i-^  not  that  the  particles  of  water  and  alcohol 
penetrate  each  other,  but  that  the  smaller  particles  occupy  a  portion 

(if   the   -pace    between    the    particles    of   tllC  Other. 

Space  utterly  devoid  of  matter  is  termed  a  vacuum. 


MOBILITY.  17 

22.  Mobility  is   that   property  by  virtue   of  which   the 
position  of  a  body  in  space  may  be  changed  on  the  applica- 
tion of  sufficient  force.     A  body  in  the  act  of  changing  its 
place  is  said  to  be  in  motion.     Rest  implies  permanence  of 
position. 

The  motion  or  rest  of  a  body  is  determined  by  its  rela- 
tion to  some  given  point;  but,  as  this  point  may  itself 
be  fixed  or  moving,  motion  or  rest  is  either  (1.)  absolute 
or  (2.)  relative. 

23.  Absolute  motion  is  a  change  of  place  with  regard  to 
a  fixed  point :    relative  motion  is  a  change  of  place  with 
regard  to  a  point  in  motion. 

Absolute  rest  is  permanence  in  place  with  reference  to  a 
fixed  point:  relative  rest  is  permanence  in  place  with  regard 
to  a  point  in  motion. 

Strictly  speaking,  there  is  no  such  condition  as  absolute  rest,  as  the 
earth  and  all  the  heavenly  bodies  are  known  to  be  in  motion.  The 
motion  of  the  heavenly  bodies  with  reference  to  ideal  fixed  points  in 
space  are  examples  of  absolute  motion.  Every  particle  on  the  earth's 
surface  partakes  of  all  the  motions  of  the  earth,  daily,  annual,  and 
cyclic,  therefore  the  terms  absolute  motion  and  rest,  when  applied  to 
bodies  on  the  earth,  have  reference  to  objects  that  appear  fixed. 

A  person  seated  on  a  steamboat  in  motion  is  in  a  state  of  relative 
rest  with  regard  to  the  parts  of  the  vessel,  but  is  in  absolute  motion 
with  respect  to  the  harbor  he  has  left,  and  to  the  water  about  him. 
If  he  walks  toward  the  stern  of  the  boat  as  fast  as  the  vessel  moves 
forward,  he  is  in  a  state  of  absolute  rest  with  regard  to  the  harbor  he 
has  left  or  the  water  around  him,  but  in  relative  motion  with  regard 
to  the  parts  of  the  boat. 

24.  The  rate  of  motion  of  a  body  is  termed  its  velocity. 
It  may  be  found  by  dividing  the  space  by  the  time.     The 
formula  [1.]   v  =  s  -t-t 

expresses  the  relation  between  space,  time,  and  velocity, 
and  may  be  used  to  find  the  third  quantity  when  the  other 
two  are  known.  From  the  formula  given,  other  formula} 
may  be  obtained;  thus,  from  [1.]  we  find  s  =  vt  and 
t  =  8  -j-  v. 

N.P.  2. 


18 


NA  T  URA  L  PHIL  OS  OP  II }  \ 


Table  of  Telocitles. 


Feet  Miles 

per  second,  per  hour. 

Man  walking 4.4  3 

Man  running 14.66  10 

Swift  trotting  horse    40.  27 

A  moderate  wind...     10.26  7 

A  storm 73.33  50 

A  rifle  ball 1466.66  1000 

Sound 1118.6  762 


Swiftest  railway  train 0.02 

Initial  velocity  of  a  can- 
non ball 0.44 

The  earth  in  its  orbit 18-97 

A  point  on  the  Equator  0.2l» 

Light 185500. 

Electricity 288000. 


25.  Inertia  is  that  property  by  virtue  of  which  a  body 
tends  to  retain  its  present  state,  whether  of  motion  or  rest. 

This  is  a  purely  negative  property  of  matter,  and  implies 
that  motion  and  rest  are  equally  natural  to  a  body.  A  body 
dropped  from  a  balloon  in  mid  air  falls  because  of  the 
earth's  attraction.  A  bullet  fired  in  the  air  does  not  stop 
because  the  explosive  force  of  the  powder  will  carry  it  no 
further,  but  because  other  forces  bring  it  to  rest. 

26.  Many  common  phenomena  may  be  explained  by  the  inertia  of 
matter.     If  a  boy  wishes  to  leap  a  broad  ditch,  he  starts  with  a  run, 
that  the   inertia  of  his  body  may  be  added  to  the  muscular  effort  of 
leaping.     With  the  same  velocity,  the  inertia  increases  with  the  weight 
of  the  body.     A  small  boy  in  running  will  easily  "dodge"  a  larger, 
because  the  heavier  boy  will  be  unable  to  change  his  course  at  once. 

If  a  person  descends  carelessly  from  a  car  in  motion,  the  upper  part 
of  the  body  retains  its  onward  motion,  while  the  feet  are  prevented 
from  doing  so  by  the  friction  of  tin-  ground,  and  lie  is  thrown  forward. 
Si i  a  person  standing  in  a  wagon  partakes 
of  its  condition  of  motion  or  rest.  If  it  is 
suddenly  started  from  a  state  of  rest,  his 
feet  are  drawn  along  by  the  friction 
.••gainst  the  bottom,  before  the  head  can 
aeijuire  the  motion,  and  the  person  tails 
i>ackward.  If  the  carriage  is  suddenly 
-topped  when  in  rapid  motion,  the  person 
is  thrown  forward. 

If  a  e;ird  is  balanced  on  the  fop  of 
one  of  the  lingers  of  the  left  hand  and  a 
penny  placed  on  it,  a  sudden  blow  given 
by  the  nail  of  the  middle  finger  of  the 


DI  VISIBILITY. 


19 


C  8   7    6    5    4   3    2  A. 


right  hand,  will  drive  the  card  away  and  leave  the  penny  on  the 
finger.  In  this  case  the  friction  of  the  card  against  the  penny  will 
tend  to  carry  it  along  with  it,  but  the  motion  communicated  will  be 
so  small  that  the  coin  will  be  moved  but  little.  This  experiment 
has  been  explained  by  saying  that  the  inertia  of  the  coin  retains  it 
in  its  place;  but  it  really  moves  a  little,  as  may  be  ascertained  by 
placing  the  card  and  penny  on  the  edge  of  a  smooth  table,  and  strik- 
ing away  the  card  as  before. 

The  inertia  of  the  air  may  be  proved  by  the  resistance  it  offers  to 
a  body  moving  through  it.  Thus,  if  we  endeavor  to  carry  an  open 
umbrella,  with  the  concave  side  forward,  we  shall  need  to  employ 
considerable  force  to  overcome  the  resistance  of  the  air.  Wind  is 
only  air  in  motion.  If  air  had  no  inertia,  it  would  not  require  force 
to  set  it  in  motion  nor  to  stop  it. 

27.  Divisibility  is   that  property  by  virtue  of  which  a 
body  may  be  divided  into  distinct  parts. 

A  geometrical  magnitude,  as  a  line, 
may  be  supposed  to  be  divided  into  an 
infinite  number  of  parts.  Let  A  B  be 
the  line  to  be  divided.  Draw  D  B 
and  A  C  at  right  angles  to  it  at  its 
extremities  and  lay  off,  on  AC,  A 2, 
23,  34,  etc.,  each  equal  to  DB,  join 
D  with  each  point,  then  D  2  will  cut 
off  one-half  of  A  B,  D3  will  cut  off 
one-third  of  A  B,  D  4  one-fourth,  etc. 
Now  as  the  line  AC  may  be  taken 

of  infinite  length,  there  is  no  limit  to  the  number  of  equal  parts 
which  may  be  taken  on  it;  consequently  there  is  no  limit  to  the 
number  of  parts  into  which  A  B  may  be  divided. 

28.  The    practical    division    of  matter   by   mechanical 
means   is    subject    to    limitation,    but   wonderfully   minute 
particles  may  be  obtained  by  repeated  subdivisions. 

Gold  may  be  hammered  so  thin  that  fifteen  hundred  leaves,  placed 
one  upon  another,  will  not  equal  the  thickness  of  a  single  leaf  of  ordi- 
nary foolscap.  The  gilt  wire  used  in  embroidery  has  a  surface  of  gold 
even  thinner  than  this.  It  has  been  calculated  that  its  thickness  does 
not  exceed  one  twenty-five  millionth  of  an  inch:  if  this  calculation  is 
correct,  then,  by  the  aid  of  a  microscope,  a  particle  of  gold  may  be 
distinguished  which  does  not  weigh  one  two-million-millionth  part  of 


FIG.  3. 


20  NATURAL  PHILOSOPHY. 

a  grain.  The  microscope  has  proved  the  existence  of  animals  not 
larger  than  the  particle  of  gold  just  mentioned,  yet  as  these  animals 
are  furnished  with  organs  of  nutrition  and  locomotion,  as  well  as  the 
larger  animals,  their  several  parts  must  be  inconceivably  small. 
Blood  is  composed  of  a  colorless  liquid  in  which  float  red,  flattened 
globules,  so  small  that  there  are  over  a  million  of  them  in  a  single 
drop. 

29.  The    wonderful    divisibility   of  matter   in    solution 
may  be  readily  shown  by  a  few  simple  experiments. 

If  a  drop  of  nitric  acid  is  allowed  to  remain  for  a  few  moments  on 
a  copper  coin,  it  will  dissolve  an  almost  imperceptible  amount  of 
copper.  Wash  the  coin  in  a  tumbler  full  of  water;  the  water  will 
hardly  be  tinged  in  color.  Now  add  some  strong  ammonia,  and  the 
liquid  will  be  changed  to  a  beautiful  blue,  showing  the  presence  of 
copper  in  every  drop  of  the  solution.  It  has  been  estimated  that  a 
single  grain  of  copper  may  thus  be  divided  into  one  hundred  million 
parts.  * 

30.  The  film  of  a  soap  bubble  before  bursting  is  less  than 
one  millionth  of  an   inch  in   thickness;    but,  as   this  film 
possesses  all  the  properties  of  water,  a  molecule  of  water 
can  not  be  more  than  a  millionth  of  an  inch  in  diameter. 
Odors  demonstrate  the  presence  of  particles  whose  size  and 
weight   must  be   infinitesimal.      A   single  grain   of   musk 
will   diffuse  a  perceptible  odor  through  a  large  room   for 
years,  without  appreciably  losing  in  weight. 

31.  Certain  facts  in  chemistry  have  led  to  the  belief  that 
there  is  a  limit  to  the  divisibility  of  mutter,  and  that  there 
are  particles  called  Atoms,  incapable  of  further  subdivision. 
By  the  conditions  of  this  hypothesis : 

32.  An  Atom  is  a  particle  of  matter  infinitely  hard,  in- 
finitely  .-mail,    and   possessing  a   definite   si/e,    shape,    and 
weight. 

Nothing  is  known  of  the  ultimate  structure  «.f  atoms,  but  it   has 

Tin-  same  facts  may  In- shown  l>y  taking  a  tiimhlrrof  water  and  add- 
ing a  drop  of  cadi  of  tin-  following  solutions  : 
1.  Sulphate  of  iron  ami  ferrocyanide  of  potassium. 
•J.   Act-tale  of  lead  and  sulphuric  acid. 
3.  Boiled  starch  and  tincture  of  iodine. 


POROSITY.  21 

been  conjectured  that  they  are  spheroidal  in  shape,  that  some  are 
larger  and  some  heavier  than  others.  That  they  are  spheroidal  in 
shape  is  a  conclusion  attained  from  the  porosity  of  bodies.  That 
they  vary  in  size  has  been  deduced  from  the  fact  that  hydrogen  will 
escape  from  a  closely  packed  piston  which  retains  oxygen  and 
nitrogen.  That  they  vary  in  weight  seems  probable,  from  the  fact 
that  the  elements  unite  in  a  definite  and  invariable  ratio  to  form 
chemical  compounds.  Thus,  if  the  atom  of  hydrogen  is  assumed  as 
unity,  the  atoms  of  the  other  elements  will  weigh  respectively : 
oxygen,  16 ;  sodium,  23 ;  iron,  56 ;  silver,  108 ;  lead,  207,  etc. 

33.  Porosity  is   that  property  by  which  spaces  exist   be- 
tween the  molecules  of  a  body. 

Pores  are  of  two  kinds,  (1.)  Physical  Pores,  which  are 
so  small  that  the  surrounding  molecules  are  at  insensible 
distances  from  each  other;  (2.)  Sensible  Pores,  which  are 
actual  cavities  or  cells  that  may  be  discerned  by  the  eye  or 
by  the  microscope ;  as  the  cells  in  bread  and  in  sponges. 

34.  In  common  language,  a  porous  body  is  one  that  con- 
tains sensible  pores.      The  porosity  of  some  woods  is  evi- 
dent to  the  eye.     The  microscope  reveals  the  presence  of 
many  thousand  pores  in  every  square  inch  of  skin  on  the 
human   hand.       Many   of  the  phenomena   of  the   organic 
world  are  due  to  the  existence  of  sensible  pores. 

The  presence  of  sensible  pores  is  turned  to  practical  use  in  filtering. 
A  piece  of  unsized  paper  is  folded  in  a  conical  shape  and  inserted  in 
a  funnel.  Liquids,  containing  suspended  matters,  having  been  poured 
into  this,  pass  through  clear,  leaving  the  solid  particles  behind.  A 
milk  strainer  acts  on  the  same  principle. 

35.  The  term  porosity,  as  applied  in  the  study  of  Natural 
Philosophy,  generally  relates  to  physical  pores.     All  bodies 
possess  these  pores,  and  it  is  supposed  that  their  atoms  do 
not  touch  each  other.    All  bodies,  with  one  apparent  excep- 
tion, expand  by  heat.      This  is  not   due  to  any  change  in 
the  size  of  the  atoms,  but  to  the  increase   of  the   spaces 
between  them.      Iron  and  lead  are  made  smaller  by  ham- 
mering, because  the  atoms  are  driven  closer  together. 

Water  may  be  shown  to  possess  pores  by  dissolving  sugar  in  a  cup 


22 


NATURAL    PHILOSOPHY. 


full  of  hot  water ;  two  or  three  spoonfuls 

may  he  added  IK- ton-  the  cnjt  overflows. 
If  a  jar  he  filled  with  alcohol  to  a  certain 
height,  a  large  quantity  of  cotton  may  he 
forced  into  it  without  raising  the  level. 
Fig.  4.  (  Jasi-s  are  so  porous  that,  if  a  ves- 
s.-l  he  filled  with  air,  another  gas  may  he 
introduced,  and  will  fill  the  vessel  as 
though  the  air  were  not  there.  The 
explanation  of  these  experiments  must 
be  that  the  atoms  of  sugar  and  water, 
alcohol  and  cotton,  or  the  two  gases,  are 
mutually  arranged  between  the  pores. 

36.  Bodies  vary  greatly  with 
respect  to  the  pores  they  contain. 
Those  that  have  many  and  large 
pores  are  called  rare  bodies;  those 
that  have  small  pores  are  called 

dense  bodies.      Fig.  5  shows  the  size  of  one  grain  of  air, 

of  water,  and  of  platinum. 

The  term  mass  is  used  to  denote  the  amount  of  matter  contained  in 
a  body.     If  gravity  were  invariable,  the  terms  mass  and  absolute  weight 


Fio.  4. 


WATER. 


SlMIKHF.   OK    Alll    WKl<;IIIMf    On    <;u.\IN. 

Fio.  5. 


SPECIFIC  GRAVITY.  23 

might  be  used  interchangeably,  as  mass  is  the  amount  of  matter  in  a 
body,  and  weight  is  the  pressure  exerted  by  it  in  consequence  of 
gravity.  The  terms  are  not  identical,  as  a  little  reflection  will  show. 
An  iron  ball  will  contain  the  same  amount  of  matter  or  mass  in  every 
conceivable  place,  but  if  it  weighs  one  hundred  and  ninety-four 
pounds  at  the  equator  it  will  weigh  one  hundred  and  ninety-five 
pounds  at  the  poles,  because,  as  will  be  shown  hereafter,  the  force 
of  gravity  varies  in  different  places. 

The  mass  of  a  body  contained  in  a  unit  of  volume  is  its 
density;  the  weight  of  the  same  unit  is  its  specific  weight. 
Hence,  mass  and  density  are  invariable  terms. 

37.  Specific  gravity  is  the  relative  weight  of  any  body 
compared  with  that  of  an  equal  volume  of  water  or  of  air. 

Air  is  the  standard  of  comparison  for  all  gases  and 
vapors,  and  water  is  the  standard  for  both  solids  and 
liquids.  The  specific  gravity  of  air  being  unity,  that  of 
chlorine  is  2.47,  of  water,  773.  The  specific  gravity  of 
water  being  unity,  that  of  air  is  .0013,  of  platinum,  21.5. 
In  other  words,  specific  gravity  is  the  ratio  which  shows 
how  many  times  heavier  a  body  is  than  an  equal  bulk  of 
air  or  of  water,  as  a  cube  of  platinum  is  21.5  heavier  than 
an  equal  bulk  of  water. 

Although  the  terms  density  and  specific  gravity  involve  different 
quantities,  they  are  used  interchangeably  without  sensible  error. 
For,  since  the  weights  of  the  water  or  air  and  the  body  to  be  com- 
pared are  ascertained  in  the  same  place,  they  will  be  alike  influenced 
by  gravity,  and  the  specific  gravity  will  be  an  invariable  quantity. 

38.  The  specific  weight  of  any  body  is  equal  to  the  pro- 
duct of  its  specific  gravity  multiplied  by  the  weight  of  the 
unit  of  water,  or  of  air,  as  the  case  may  require:  thus,  for 
liquids  and  solids : 

[2.]     Sp.  W.  =  998.7  oz.  X  Sp.  Gr. 

Since  the  weight  of  a  cubic  foot  of  water  is  nearly  1,000 
ounces,  that  of  the  same  bulk  of  any  solid  or  liquid  is 
nearly  as  many  thousand  ounces  as  are  denoted  by  its  spe- 
cific gravity. 


24  NATURAL   PHILOSOPHY. 

The  mass  of  any  body  is  equal  to  the  product  of  its 
density  and  volume;  its  absolute  weight  is  equal  to  the 
product  of  its  specific  weight  and  volume. 

Therefore  for  cubic  feet  of  either  liquids  or  solids 

[3.]  W  =  V  X  Sp.  W.  =  V  X  Sp.  Gr.  X  62.42  Ibs. 
Thus  the  weight  of  a  cubic  yard  of  lead  is 

27  X  H.35  X  62.42  =  19,128  pounds. 
For  aeriform  bodies  whose  volume  is  stated  in  cubic  inches, 

[4.]  W  =  V  X  Sp.  Gr.  X  0.31  grains. 
Thus  the  weight  of  a  gallon  of  chlorine  is 

231  X  2.47  X  0.31  =  176.87  grains. 

39.  The  method  of  finding  specific  gravity  will  be  given 
in  its  proper  place.  As  there  will  be  frequent  occasion  to 
refer  to  specific  gravity,  a  table  of  the  most  important  sub- 
stances is  inserted  at  this  point: 

Specific  Gravities  Compared. 

32°  F.  62°  F. 

Ratio  of  air  to  water 1  to  773.2  1  to  816.8 

Ratio  of  water  to  air 1  to        .00129363        1  to        .0012243 

One  cubic  inch  of  air  at  60°  F.  weighs  0.30954  grains. 

One  cubic  inch  of  water  at  60°  F.  weighs  252.456  grains. 

Specific  Gravity  of  the  same  Body  in  different  States. 

Air  =  l.  Water  =1. 

Gases.  Liquid.  Solid. 

Ammonia 0.596  0.731 

Carbonic  acid 1.529  0.83 

<  •hlorine 2.47  1.33 

Sulphurous  :icid 2.247  1.38 

As  Vapors. 

Alcohol 1.613  0.792 

Ether 2.589  0.715 

Water 0.622  1.  <).'.»:; 

Mercury <;."7«;  13.596  l.V.'.is 

Iodine s.Tir,  l.'.M* 

Sulphur 2.230  2.086 


l! 

if 


COMPRESSIBILITY. 


25 


Table  of  Specific  Gravities. 


GASES. 

Air 1. 

Hydrogen 069 

Nitrogen 972 

Oxygen 1.106 

LIQUIDS. 

Water,  distilled 1. 

Sea  water , 1.026 

Olive  oil 0.915 

Sulphuric  acid 1.84 


SOLIDS. 

Cork 0.24 

White  oak 0.86 

Ebony 1.331 

Glass 3. 

Potassium 0.86 

Platinum 21.53 

Gold 19.26 

Silver 10.5 

Copper 8.85 


Iron. 
Lead 


.  7.78* 
.11.35 


Saturated  brine 1.205    Iron  pyrites 5. 

40.  Compressibility  is  that  property  by  virtue  of  which 
the  volume  of  a  body  may  be  diminished. 

This  is  a  consequence  of  porosity.  Rare  bodies  are  much 
more  compressible  than  dense  bodies.  Gases  may  be  made 
to  occupy  a  hundred  times  less  space  than  they  do  under 
ordinary  circumstances.  Many  gases,  under  great  pressure, 
become  liquids;  others,  as  oxygen,  nitrogen,  and  air,  seem 
to  have  no  limit  to  their  compressibility.  Liquids  possess 
this  property  in  so  limited  a  degree  that  they  were  once 
supposed  to  be  incompressible.  Solids  are  all  compressible. 

41.  Expansibility    is    the    converse    of    the    preceding. 
The    volume    of    all    bodies,    except    clay,     is    increased 
by   heat.      With    equal   incre- 
ments   of  heat,  gases    expand 

most,  liquids  next,  and  solids 
least. 

When  a  diving-bell  is  sunk  in  the 
sea,  the  water  compresses  the  air 
and  rises  within  the  bell  to  a  certain 
height,  although  it  can  not  fill  the 
bell  because  the  air  is  impenetrable, 
When  the  bell  is  raised,  the  air  ex- 
pands and  recovers  its  former  vol- 
ume. If  a  flask  is  nearly  filled  with  FIG.  6. 


26  NATURAL   PHILOSOPHY. 

water  and  then  inverted  in  a  basin,  a  little  air  will  be  inclosed  at  the 
top  of  the  flask.  If  the  Husk  is  wanned,  the  air  expands  and  expels 
a  portion  of  the  water.  On  cooling  the  flask,  the  air  resumes  its 
former  bulk. 

42.  Various   units  have  been  adopted  for  the  measure- 
ment  of    intensity   of    pressure.     Thus,   pressure   may    be 
estimated  at  so  many  pounds  to  the  square  inch,  or  to  the 
square   foot.     The   pressure  of  one   atmosphere    is   a   unit 
in   very  common    use.     The  atmosphere  presses    on   every 
square  inch  of  all  surfaces  at  the  level  of  the  sea  with  a 
force  of  about   fifteen   pounds,    hence    all   other  pressures 
may  be  taken  as  so  many  times  greater  or  less  than  this, 
or,  as  so  many  atmospheres. 

Units  of  'Pressure. 

I'uii lulu  on  each        Pounds  on  each  In 

>'jti:in- inrli.  square  foot.      atmospheres. 

Water,  1  foot  deep,  at  39°.2  F.~  0. 1335  r>2.42:>  0.02l)o 

Water,  1  foot  deep,  at  62°  F 0.4330  152.355  0.0294 

30  inches  mercury,  at  <>2°  F 14.7225  2120.  1. 

1  inch  mercury,  at  .",2°  F 0.4912  7o.7:j  0.0334 

1  foot  of  air,  at  32°..  O.ooiMi  0.0807  0.00004 

1  pound  to  the  square  inch.  2.:J  ft.  water.  2  in.  mercury.  0.008 

43.  Indestructibility  is  that  property  by  virtue  of  which 
a  substance  resists  annihilation. 

Whatever  changes  man  may  impose  upon  matter,  it  still  continues 
in  Mime  form,  and  may  at  any  time  he  recoirni/.ed  as  matter.  Thus, 
all  the  change-  ih-erihed  in  i  S.  >  caused  no  loss  in  the  substances  acted 
upon.  Wood,  in  burnini:,  pa.—es  away  in  smoke,  leaving  only  a 
.-mall  propi.riiiin  <>f  a.-hes;  yet  the  a>he-  and  the  Mnoke  contain  all 
the  mutter  nf  the  wood. 

SPKCIFIC    PROPERTIES    OF    MATTER. 

44.  Most  of  the   specific  properties   of   matin-   are  de- 
pendent un  the  molecul&r  attractions,  aflinitv,  cohesion,  and 

adliesiim,  modified  by  the  molecular  repulsion  of  heat  and. 
perhaps,  of  electricity. 


ADHESION.  27 

45.  Affinity   is   that    force   which    causes    the    atoms    of 
unlike  substances  to  unite  and  thus  form  new  bodies. 

For  example,  when  a  nail  is  exposed  to  moist  air,  the  iron  combines 
with  the  oxygen  of  the  moisture  and  forms  a  coating  of  rust,  which 
is  an  oxide  of  iron. 

46.  Adhesion  is  the  force  which  causes  the  molecules  of 
different  kinds  of  matter  to  cling  together. 

Thus,  adhesion  causes  the  dust  to  cling  to  every  thing  it 
falls  upon,  chalk  to  cling  to  black-boards,  mud  to  clothing, 
dew  drops  to  leaves,  and  icicles  to  eave-troughs.  Under 
the  name  of  Friction,  it  diminishes  the  work  of  moving 
forces,  (1.)  by  stiffening  the  joints  of  machines,  and  (2.) 
by  increasing  the  resistance  to  be  overcome.  Friction  often 
acts  as  a  mechanical  advantage,  as  in  preventing  our  feet 
from  slipping  when  standing  or  walking,  in  retaining  nails 
and  screws  in  their  sockets,  and  in  enabling  locomotives  to 
ascend  gradients. 

47.  The  force   of  adhesion  gives  value  to  the  cements. 
No   better  proof  can    be   desired  that  adhesion  is   not  the 
same  for  all  substances,  than  the  great  variety  of  cements 
employed   for  different   materials;    thus,   glue   is   used   for 
wood,    the  gum   resins    for   glass,    mortars   for  brick,    etc. 
The  adhesion  of  good  glue  and  of  the  best  hydraulic  cements 
is  about  five  hundred  pounds  to  the   square  inch,  that  of 
ordinary  mortars  is  much  less. 

48.  Cohesion  is  the  force  which  causes  like  molecules  to 
unite  in   one  mass.     This  force   retains  the  particles  of  a 
cannon  ball  or  of  a  lump  of  ice  in  a  single  piece.      It  is 
strongly  exerted  in  solids,  less  strongly  in   liquids,  and   is 
entirely  absent  in  aeriform  bodies. 

Liquids.  In  large  masses  of  liquids  the  force  of  cohesion 
is  overcome  by  the  force  of  gravity,  which  tends  to  bring 
all  their  molecules  to  the  same  level ;  in  very  small  masses 
the  cohesive  force  is  the  stronger,  and  causes  them  to 
assume  a  spheroidal  form. 


28  NATURAL   PHILOSOPHY. 

This  is  shown  in  drops  of  dew,  in  globules  of  mercury,  and  in 
small  drops  of  water  rolling  upon  a  dusty  table.  The  same  fact  is  ex- 
emplified in  the  following  pretty  experiment:  fill  a  tall  wine-glass 
half  full  of  water  and  earei'iilly  pour  upon  the  water  an  equal 
quantity  of  alcohol  so  as  not  to  mix  the  two  liquids,  then  drop  a 
very  little  olive  oil  through  the  alcohol ;  it  will  assume  the  shape  of 
a  spheroid  and  rest  in  the  middle  of  the  glass.  The  experiment  may 
be  made  more  striking  by  pouring  into  a  clear  glass  bottle  half  full 
o!'  a  saturated  solution  of  sulphate  of  zinc,  some  distilled  water,  and 
dropping  through  the  water  a  little  bisulphide  of  carbon,  colored  by 
iodine.  The  spheroid  may  be  made  larger  than  the  neck  of  the 
bottle. 

Solids.  When  the  cohesion  of  solids  has  been  once 
destroyed  it  is  often  difficult  to  cause  the  particles  to  re- 
unite. 

Broken  metallic  castings  may  be  remelted,  and  made  to  cohere  in 
the  same  or  a  different  form  on  cooling.  Particles  of  loose  sand 
jammed  forcibly  together,  as,  for  instance,  by  a  cannon  ball,  will 
cohere  like  stone.  In  like  manner  broken  ice  can  be  cemented 
together  in  one  transparent  mass  by  pressure.  Two  dull  leaden  bul- 
lets will  not  unite  because  the  surface  is  covered  by  the  oxide;  but  if 
each  be  cleanly  cut  by  a  sharp  knife  so  as  to  present  a  smooth  and 
bright  surface,  they  will  unite  on  being  pressed  tightly  together,  with 
a  slight  twisting  motion.  Two  plates  of  polished  glass  will  cohere, 
under  pressure,  so  forcibly  that  they  may  be  worked  as  a  single  piece. 
The  slightest  film  of  paper  or  even  dust  is  sufficient  to  prevent  this 
action. 

49.  Adhesion  and  cohesion  differ  from  affinity  in  this, 
that  their  action  on  bodies  does  not  effect  any  essential 
change  in  the  properties  of  the  bodies.  They  differ  from 
cadi  other  in  this,  that  adhesion  acts  between  unlike  par- 
tides,  and  cohesion  between  like  particles. 

Heat  generally  increa.-es  the  force  <,f  afiinity,  Itut  it  tends  to  weaken 
the  force  of  ci.hoion.  It  is  probable  that  all  >olids  may  be  converted 
to  liquids,  and  even  to  vapor-,  by  sullicient  heat,  and  that  all  gases 
and  liquids  may  !•••  rh:m.ir«-d  to  solids  by  a  .-uflicicnt  reduction  of  tem- 
perature, a  — i-ted  by  pre-^ure,  although  then'  are  many  solids  that 
have  not  been  liquefied,  and  many  gases  that  have  hitherto  resisted 
all  endeavors  to  charge  their  state. 


COHESION.  29 

50.  The   cohesion   of  the   particles  of  a  solid  may  be 
estimated  l>y  the  kind  and  amount  of  resistance  which  its 
particles  offer  to  a  strain  tending  to  rend  them.     The  force 
which  causes  the  strain  may  be  applied 

I.  In  the  direction  of  the  length  of  the  body : 

(1.)  By  a  direct  thrust,  as  when  a  weight,  resting  on  a 
column,  tends  to  crush  it. 

(2.)  By  a  putt,  as  when  a  weight,  stretching  a  string, 
tends  to  tear  it  in  pieces. 

II.  Transversely,  or  across  the  length : 

(3.)  By  bending,  as  when  a  bow  is  strained  and  tends  to 
break. 

(4.)  By  twisting,  when  the  strain  tends  to  wrench  the 
particles  asunder. 

III.  A  body  may  be  subjected   to   several  strains  at  the 
same  time. 

51.  These  relations  are  made  more  evident  by  the  follow- 
ing table: 

Direction  of  force.  Kind  of  stress.          Kind  of  strain.  Kind  of  fracture. 

I    Longitudinal.  ((L)  Thrust  Compression.  Crushing. 

I  (2.)  Pull.  Stretching.  Tearing. 

II.  Transverse.   { ^  BendinS-  Bending.  Breaking. 

<>  (4.)  Twisting.          Torsion.  Wrenching. 

III.  Combined.      (5.)  Distortion.        Detrusive.  Shearing. 

52.  Experience  teaches  that  the  effect  produced  by  any 
strain  will  vary  greatly  with  the  material  on  which  it  acts, 
as  well  as  with  the  intensity  of  the  force.     Thus,  a  sufficient 
force   will   cause   fracture  in   any  solid;    a  less  force  may 
produce  a  permanent  or  a  transient  change  in  its  shape. 

53.  Elasticity  is  the  property  by  virtue  of  which  bodies 
altered   in    form    or  volume   by  any  external   force,  resume 
their  original  shape,  when  that  force  has  ceased  to  act. 

The  change  of  form  or  volume  is  due  to  the  strain, 
which  compresses,  stretches,  bends,  or  twists  the  body.  The 


30  NATURAL   PHILOSOPHY. 

energy  with  which  the  particles  resume  their  original  posi- 
tion, is  due  to  their  elastic  force.  Up  to  a  certain  limit, 
which  varies  with  the  substance,  the  elastic  force  is  exactly 
equal  to  the  stress,  and  the  elasticity  is  therefore  perfect. 
Beyond  that  limit,  brittle  bodies  break;  the  molecules  of 
most  other  solids  are  forced  into  new  relations  with  each 
other,  by  which  the  bodies  assume  a  permanent  change,  or 
set,  with  new  relations  to  elasticity  similar  to  the  first. 
Thus,  when  a  wire  has  been  permanently  lengthened  by  a 
<rrcat  strain,  it  is  still  enabled  to  manifest  perfect  elasticity 
by  recovering  from  a  smaller  strain. 

The  elasticity  developed  by  pressure  belongs,  in  some 
degree,  to  all  bodies,  whether  solid,  liquid,  or  gaseous,  and 
is,  therefore,  a  general  property  of  matter.  The  other 
forms  of  elasticity  belong  only  to  solids. 

54.  Compression.     The   elasticity   of  aeriform    bodies   is 
exemplified  by  a  boy's  pop-gun.     The  air  between  the  wad 
and  the  piston,  being  compressed  by  the  piston,  increases  in 
elastic  force  as  it  decreases  in  volume,  until   the  elasticity  is 
sufficient  to  expel  the  ball. 

The  air  near  the  earth's  surface  is  compressed  by  all  the 
air  above  it.  If  a  portion  of  the  air  is  confined  in  the 
receiver  of  an  air  pump,  and  the  pressure  removed  by 
working  the  pump,  the  elastic  force  of  the  air  remaining, 
though  lessened  by  every  stroke,  is  always  sufficient  to  fill 
the  receiver.  From  their  perfect  elasticity  under  increased 
and  diminished  pressure,  aeriform  bodies  have  received  the 
name  of  clastic  fluids. 

55.  Liquids   are   sometimes  called  the  non-elastic  fluids, 
but    the     name    is    applied    erroneously,    from     a     mistaken 
notion  of  their  incomprcssihility.      Whenever  the  force  that 
compn--r>  them   is  removed,   they  immediately  retrain   their 
original   volume;    therefore,  all  J ln'nl.<  arc  j>n-frrtl//  rln#tic.. 

56.  Solids    possese    this    property    in    different    degrees. 
India    rubber,    ivory,   ^lass,    and    marble    have    considerable 
elasticity;    lead,  clay,  and  fats  have  very  little. 


STRENGTH.  31 

If  a  ball  of  ivory  or  of  glass  be  dropped  on  a  slab  of  marble,  it 
will  rebound  to  a  height  nearly  equal  to  that  from  which  it  fell. 
If  the  slab  had  been  smeared  with  oil,  it  would  be  found  that  the  ball 
had  left  a  circular  impression  on  the  plate,  and  had  itself  received  a 
blot  of  oil;  on  repeating  the  experiment,  it  will  be  seen  that  the  size 
of  the  spot  on  the  table  and  on  the  ball  increases  with  the  height 
from  which  it  falls.  From  this  experiment  it  appears  (1.)  that,  at  the 
moment  of  shock,  the  ball  was  compressed,  (2.)  that  its  rebound  was 
caused  by  the  effort  to  regain  its  original  shape,  and  (3.)  that  its 
elastic  force  increases  with  the  strain. 

57.  The  elasticity  of  traction  is  shown  by  the  strings  of 
musical  instruments,  which  are  made  more  or  less  tense,  by 
stretching,  at  the  will  of  the  performer. 

58.  Flexibility  should  not  be  confounded  with  elasticity. 
A  wire  of  soft  iron  is  very  flexible,  though  but   slightly 
elastic.     A  steel  sword  blade  has  been  bent  double  and  on 
the  removal  of  the  force,  has  straightened  itself  perfectly, 
showing  that  it  is  both  flexible  and  elastic.    Threads  of  glass 
are  even  more  elastic  than  steel,  though  not  as  flexible. 

59.  The  elasticity  of  torsion  is  manifested  in   the  ten- 
dency that  twisted  yarns  and  strings  have  to  untwist. 

60.  The  practical  applications  of  the  elasticity  of  bodies 
are    innumerable.      The    elasticity   of   aeriform    bodies    is 
turned  to  account  in  foot  balls,  air  cushions,  springs,  etc. 

The  elasticity  of  solids  is  applied  in  the  springs  used  in 
watches,  clocks,  carriages,  bows,  balances,  etc.  The  value 
of  corks  is  due,  in  great  measure,  to  their  elasticity. 

61.  The  ultimate  strength  i>  the  cohesion  with  which  a 
body    resists   a   stress    tending   to   produce   fracture.      The 
proof  strength  equals  the  greatest  strain  that  may  be  borne 
with  safety;    it  varies  from  one-tenth  to  two-thirds  of  the 
ultimate  strength.     The   kind    of  strength   which   a   body 
manifests   in   any   instance,    is    called  its   resistance   to   the 
strain  employed;   as   n-Mstance  to  compression,  etc.,  except 
that: 

The  resistance  which  bodies  offer  to  forces  tending  to  pull 
their  particles  apart  is  called  Tenacity. 


32 


NATURAL   PHILOSOPHY. 


62.  All  kinds  of  strength  increase,  to  a  greater  or  less 
degree,  with  the  area  of  the  cross  section  of  the  body,  and 
all,  except  tenacity,  decrease  when  the  length  is  increased. 
The  only  effect  of  increase  of  length  upon  tenacity  is  that 
the  weight  of  the  body  is  added  to  its  load.  The  annexed 
table  shows  the  comparative  strain,  expressed  in  pounds 
avoirdupois,  that  may  be  borne  by  rods  not  exceeding  a 
foot  in  length  and  whose  cross  section  is  one  square  inch. 
The  first  column  shows  the  force  required  by  theory  to 
double  the  length  of  the  bars,  a  thing  impossible  to  be 
done,  except  in  the  case  of  india  rubber. 

63.  Table. 


Materials. 

M.  "lulus 
of 
elasticity. 

Resistance  to  fracture. 

By   crushing. 

Tenacity. 

By  breaking. 

By  wrencli'g. 

\<h 

1600000 
1750000 
1460000 
22900000 
29000000 
42000000 
18240000 
720000 

9000 
10000 
6200 
112000 
40000 
295000 
117000 
7700 

17000 
19800 
12000 
29000 
70000 
130000 
36000 
3300 

168 

245 
160 
980 
700 
1918 

1460 
2350 
1540 

O-ik 

Pine                 

Iron  bur.      ..      

Steel 

Copper   

64.  From   this   table,   it   will   be  seen   that   the   greatest 
strength  of  materials,  except  of  wrought  iron  and  timber, 
lies  in  their  power  to  resist  compression.     The  values  given 
in    the   table  can  not  be  regarded  as   absolutely  accurate, 
inasmuch  as  it  is  extremely  difficult  to  obtain  specimens  for 
cxj>crii)icnt    which    shall    exactly  represent   the   strength   of 
the  material,  and  also  because  slight  imperfections  and  im- 
purities  of   tin-    material    produce    marked    change    in    the 
result.     The  following  deductions  from  many  experiments 
are,  however,  of  general  application: 

65.  The  strength  of  a  fabric  depends  not  only  (1.)  on 
the  nature  of  the  materials,  as  has  been  shown;   but,  also, 


STRENGTH.  33 

(2.)  on  the  distribution  of  the  strain,  and  (3.)  on  the  mode 
in  which  the  materials  are  arranged. 

The  long  continued  action  of  a  small  strain  will  often 
produce  fracture  in  a  bar  that  would  originally  have  re- 
sisted a  much  greater  force  for  a  short  time.  Every 
strain  that  exceeds  the  limit  of  elasticity  tends  to  weaken 
the  substance,  until  at  last  it  yields  readily.  A  continual 
jarring  or  pounding  so  alters  the  molecular  condition  of 
iron,  that  after  a  while  it  becomes  extremely  brittle ;  for 
this  reason  axles  in  carriages  and  railway  cars  should  be 
subjected  to  frequent  tests.  A  sudden  shock  causes  a 
greater  strain  than  a  continued  force  of  equal  amount.  A 
horizontal  beam,  supported  at  both  ends,  will  sustain  twice 
the  force,  when  distributed  throughout  its  length,  that  it 
will  when  concentrated  at  the  center. 

66.  It    has    been   demonstrated   that   the   most 
advantageous  form   for  iron  beams  is  one  which 
has  its  greatest  depth  at  the  center,  and  a  cross 
section   resembling   Fig.    8.      Of  two  rectangular 
beams,  having  the  same  area,  that  which  has  the       FIG.  a. 
greatest  depth  will  be  the  stronger :  for  this  reason,  beams 
and  rafters  are  placed  so  as  to  receive  the  stress  on  their 
edges. 

The  most  economical  arrangement  of  a  given  mass  of  ma- 
terial is  that  of  a  hollow  tube.  This  arrangement  is  seen  in 
the  bones  of  animals,  stalks  of  grain,  and  quills  of  birds.  A 
hollow  cylinder  may  be  made  of 
twice  the  strength  of  a  solid 
cylinder  containing  an  equal 
weight  of  the  same  material. 
An  easy  illustration  of  this  fact 
may  be  had  by  resting  the  ends 
of  a  flat  sheet  of  paper  on  sup- 
ports and  ascertaining  the  force  FIO. 
necessary  to  break  it  down ;  and  then  repeating  the  test 
after  having  coiled  the  paper  into  a  tube. 

N.  P.  3. 


34  NATURAL    PHILOSOPHY. 

67.  A  hollow  rectangular  tube,  whoso  height  considerably 
exceeds  its  breadth,  is  stronger  than  a  round  tube  of  the 
same  mass.     This  form  is  applied  in  the  Victoria  bridge,  at 
Montreal,  and  in  the  Great  Eastern  steamship. 

The  center  tube  of  the  Victoria  bridge  is  three  hun- 
dred and  thirty  feet  long,  sixteen  feet  broad,  and  nearly 
twenty-two  feet  high.  It  is  made  of  boiler  iron,  about  one 
half  inch  in  thickness,  and  strongly  braced  with  lateral 
irons.  The  ordinary  pressure  of  a  railway  train  passing 
through  it  is  scarcely  noticeable. 

68.  The  tenacity  of  a  substance  is  increased  by  drawing 
it  into  the  form  of  a  wire.     Hence,  cables  made  of  fine 
iron  wire  twisted  together,  are  far  stronger  than  chains  of 
equal  weight,  and  are  now  coming  into  general  use.     There 
are  many  suspension  bridges  in  this  country  and  in  Europe 
made   of  wire  cables.      The  suspension   bridge   across  the 
Ohio  river  at  Cincinnati,  has  a  span  of  one  thousand  feet. 

69.  If  wood  were  as  durable  as  iron,  its  lightness  would 
make   its  use  preferable  in   all  cases  where  tenacity  is  re- 
quired.    Thus,   pine,   which  has   nearly  half  the   tenacity, 
has   only  one   tenth  the  weight  of  cast   iron ;  so   that,  for 
equal  weights,  pine  has  more  than  four  times  the  tenacity 
of  cast  iron. 

It  would  be  impossible  to  build  such  roofs  and  bridges  of  iron  as 
have  been  built  of  timber,  because  the  strength  of  the  material  would 
not  be  sufficient  to  support  its  own  weight.  It  is  evident  that  the 
effective  strength  of  any  fabric  is  merely  that  which  is  not  employed 
in  supporting  itself,  and  that  when  a  certain  size  is  passed,  every 
additional  part  only  adds  to  the  load  without  increasing  the  strength, 
and  thus  weakens  the  whole.  For  this  n-Msmi  m:my  inventions,  that 
:ippi-ar  faultless  in  model,  fail  when  made  of  full  si/c. 

70.  There  is  therefore   a  limit   of  magnitude  which   no 
structure,  natural  or  artificial,  can  .surpass,  so  long  as  their 
materials  are  unchanged.     Thus,  insects  arc  proportionally 
stronger  than  mammals,  the  smaller  quadrupeds  are  capable 


HARDNESS.  35 

of  feats  of  strength  and  agility  impossible  to  the  larger. 
Whales  would  be  incapable  of  motion  if  their  enormous 
weight  were  not  sustained  by  the  buoyancy  of  the  ocean. 

71.  The  hardness  of  a  body  is  measured  by  the  readiness 
with  which  it  is  worn  or  scratched  by  another  substance. 

For  the  purpose  of  determining  the  relative  hardness  of  minerals, 
the  following  arbitrary  scale  has  been  adopted,  in  which  any  sub- 
stance is  scratched  by  those  below  it  : 

Scale  of  Hardness  of  Minerals. 

1.  Talc,  4.     Fluor  spar,  7.  Quartz, 

2.  Gypsum,  5.     Apatite,  8.  Topaz, 
2.5  Mica,  5.5  Sea  polite,  9.  Sapphire, 

3.  Calc-spar,  6.     Feldspar,  10.  Diamond. 

72.  A  body  which  neither  scratches  nor  is  scratched  by 
any  given  mineral  of  the  table,  is  said  to  be  of  the  degree 
of  hardness  represented  by  that  mineral.     Thus,  there  are 
fifty-three  minerals  whose  hardness  is  4,  or  equal  to  fluor 
spar.     The  diamond  can  be  cut  only  by  means  of  its  own 
powder;    talc,   or   soapstone,  is  easily  cut  with  the  thumb 
nail.     Few  of  the  metals  are  as  hard  as  glass;    some,  as 
lead  and  potassium,  are  very  soft,  and  mercury  is  a  fluid, 
from  which  it  appears  that  hardness  bears  no  relation  to  the 
density  of  a  body.     As  a  general  thing,  metals  are  softer 
than  their  alloys. 

73.  Brittleness    is   the    property   which   renders   a   body 
capable  of  being  easily  broken  or  pulverized.     Thus,  hard 
bodies   are  generally  brittle,   and   so   too   are   most  elastic 
bodies,  when  the  limit  of  elasticity  has  been  exceeded. 

74.  Ductility  is  the  property  by  virtue  of  wrhich  a  body 
may  be  drawn  into  wire.     Platinum   has   been  drawn  into 

aoooo  °f  an  incn  iQ  diameter. 


75.  Malleability  is  the  property  by  virtue  of  which  bodies 
may  be  rolled  or  hammered  into  sheets.  Gold  leaf  may  be 
made  less  than  -  °f  an  incn  thick. 


36 


NATURAL  PHILOSOPHY. 


Most  metals  are  both  malleable  and  din-tile,  though  not  in  equal 
degrees.  Antimony,  bismuth,  and  some  others,  have  neither  pro- 
perty. 

76.  Some  metals  are  most  readily  malleable  under  the 
hammer  and  others  under  rollers.  Elevation  in  tempera- 
ture is  generally  attended  with  an  increase  of  malleability 
and  ductility ;  copper,  and  its  alloys,  and  lead  being  the 
prominent  exceptions.  Iron  and  glass  are  very  malleable 
and  ductile  at  a  red  heat.  Zinc  can  be  rolled  with  best 
success  at  a  temperature  between  226°  F.  and  300°  F. 
Although  the  tenacity,  ductility,  and  malleability  of  metals 
are  alike  dependent  on  the  force  of  cohesion,  yet  the  same 
metal  does  not  always  manifest  the  same  relative  degree  of 
each,  as  may  be  seen  by  the  following  table: 


Tenacity. 

Ductility. 

Malleability. 

Under  tin-  l.amni.T. 

Under  rollers. 

1.  Iron, 

Platinum, 

Lead, 

Gold, 

2.  Copper, 

Silver, 

Tin, 

Silver, 

3.  Platinum, 

Iron, 

Gold, 

Copper, 

4.  Silver, 

Copper, 

Zinc, 

Tin, 

5.  Zinc, 

Gold, 

Silver, 

Lead, 

6.  Gold, 

Zinc, 

Copper, 

Zinc, 

7.  Lead, 

Tin, 

Platinum, 

Platinum, 

8.  Tin. 

Lead. 

I  ron. 

Iron. 

77.  Some  of  the  effects  of  heat  upon  cohesion  have 
already  been  noticed.  Among  the  permanent  changes  pro- 
duced by  heat  are : 

(1.)  HARDENING.  Many  substances,  if  suddenly  cooled 
after  having  been  strongly  heated,  become  harder,  more 
brittle,  and  more  elastic  than  before.  If  steel  is  raised  to 
a  white  heat  and  then  plunged  into  a  bath  of  cold  water  or 
mercury,  it  is  rendeivd  almost  as  hard  as  the  diamond,  very 
ela.-tie,  and  so  brittle  that  it  is  suitable  only  for  the  di<-> 
used  in  coining  and  en^raviii.ir,  and  lor  the  hardest  files. 

(2.)  BOFTENDrO.  Metals  and  jrlass  are  annealed  by  being 
slowly  cooled  from  a  hid)  temperature.  Annealing  gen- 


37 

orally  increases  the  flexibility,  softness,  and  ductility  of 
bodies.  When  metals  have  become  brittle  through  excess 
of  strain  in  rolling,  wire  drawing,  twisting,  hammering,  or 
other  mechanical  means,  their  properties  may  be  restored  by 
annealing. 

(3.)  TEMPERING.  Steel  is  wrought  into  any  form  required 
in  the  arts  when  it  is  in  its  softened  condition.  It  is  then 
strongly  heated  and  suddenly  cooled,  but,  as  this  hardening 
procsss  renders  it  too  brittle  for  ordinary  purposes,  some- 
thing of  its  elasticity  is  sacrificed,  and  a  portion  of  its 
hardness  removed  by  reheating  the  steel  to  a  lower  temper- 
ature and  then  cooling  it  gradually.  This  process  of  an- 
nealing is  called  drawing  the  temper,  or  tempering.  The 
temper  required  depends  on  the  use  to  which  the  steel  is  to 
be  applied,  and  may  be  regulated  by  varying  the  tempera- 
ture of  the  second  heating;  the  higher  the  heat,  the  softer 
will  be  the  steel. 

If  a  steel  knittiug  needle  be  hardened,  then  brightened  and  re- 
heated, the  film  of  oxide  on  its  surface  becomes,  at  a  temperature  of 
428°  F.,  of  a  light  straw  color,  then  through  intermediate  hues  to 
violet  yellow  (509°  F.),  blue  (560°  F.) ;  at  977°  F.  the  steel  passes  to 
a  red  heat.  These  colors  guide  the  workman  in  the  effects  he  wishes 
to  produce.  Light  yellow  indicates  the  heat  required  for  surgical 
instruments,  in  which  a  keen  edge  is  required  ;  a  deeper  yellow,  fine 
cutlery;  violet  is  the  tint  for  table  knives,  requiring  flexibility  more 
than  a  hard  but  brittle  edge;  blue  for  springs,  sword  blades,  and 
other  flexible  instruments. 

78,  The  effect  of  rapid  or  slow  cooling  of  glass  is  about 
the  same  as    in  steel.      Melted  glass  dropped  into 
water    solidifies    into    the    curious    toy   knows    as 
Prince  'Rupert's  drops.     The  body  of  these   drops 
is  so  hard  that  it  will  bear  a  smart  blow;    but   if 
the    tail    be    broken,  the    whole    flies    into  minute 
particles  with  considerable  violence.     This    brittle-      Fl°- 10- 
ness  is  prevented  in  glass  utensils  by  careful  annealing.     As 
soon  as  glass  vessels  are    blown   they  are  placed  in  a    long 
furnace,  in    which  the    heat,  at   first  very  great,  gradually 


38 


NATURAL  PHILOSOPHY. 


diminishes  from  one  end  to  the  other.  Through  this  fur- 
nace they  are  slowly  drawn,  and  thereby  are  cooled  so 
gradually  and  equably  that  their  molecules  assume  the  most 
stable  position  with  regard  to  each  other,  and  all  are  alike 
affected  by  any  shock. 

Heat  produces  on  copper  and  bronze,  effects  precisely  the 
reverse  of  those  manifested  by  steel.  When  they  are  cooled 
slowly  they  become  hard  and  brittle,  but  when  cooled 
rapidly,  soft  and  malleable. 


79.  Recapitulation, 


Properties  of  matter : 

Essential. 


Universal. 


Specific. 


,  Extension, 

\  Impenetrability. 

(  Weight, 
Mobility, 
Inertia, 
Divisibility, 
Porosity, 
Compressibility, 
Expansibility, 
Indestructibility, 

-  Elasticity. 

j  Elasticity, 

(Tenacity. 

C  Hanlix 

Involving  permanent  displace-      Brittleness, 
ment  of  particles.  1  Ductility, 

I  Malleability. 


General. 


Involving  strain  of  particles. 


PHENOMENA    CONNECTED   WITH   ADHESION. 

80.  Two  facts  relating  to  the  force  of  adhesion  have 
already  been  noticed:  (1.)  that  it  exists  only  between 
unlike  molecules;  (2.)  that  it  varies  with  the  kind  and 
the  >tate  of  matter.  To  these  may  be  added,  (3.)  that  it 
increase-  with  the  number  of  molecules  in  contact.  As 
only  the  exterior  particles  of  solids  can  hi-  brought  in  con- 
tact with  others,  this  statement,  when  applied  to  solids  at 
rest,  become.-., 

Adhesion  increases  with  the  extent  of  surface. 


ADHESION. 


39 


81.  With  regard  to  the  second  fact,  it  is  evident  that,  as 
there  are  only  three  states  of  matter,  all  the  possible  varie- 
ties of  adhesion  must  fall  into  some  one  of  their  combina- 
tions, taken  two  and  two.  It  will  be  convenient  to  indicate 
these  by  Roman  numerals,  thus: 


T. 


IV. 

f  Solids  to  gases. 

iquids.    -,    v  Gases  to  solids. 
VI. 

solids.    J 


Solids  to  solids. 
II. 

{Solids  to  liquids. 
III. 
Liquids  to  solids.    J       Liquids  to  liquids. 


VII. 

Liquids  to  gases. 

VIII. 
Gases  to  liquids. 

IX. 
Gases  to  gases. 


82.  The  adhesion  of  solids  to  solids  has  found  sufficient 
illustration    in  cements  and   in   friction   (46,  47).     As  all 
attractions    are    mutual,    it    is    hardly    necessary    to    make 
any    distinction    between    the    three    pairs    connected    by 
braces,  except  it  be  for  the  purpose  of  giving  prominence  to 
either  body  in  any  special  case.     Thus,  when  lycopodium 
or  powdered   resin    is   strewn   in   patches  on  a  board,  and 
water  is   sprinkled   upon   it,    (II)   the  drops   that   fall    on 
the    powder  attract   the   particles    to    themselves   and    roll 
about  in  globules,  covered  by  the  adherent  solid ;   (III)  the 
drops  that  strike  the  clean  surface  of  the  board  adhere  to 
it  and  flatten.     Either  case  illustrates  the  adhesion  between 
the  solid  and  the  liquid. 

Some  of  the  nine  varieties  of  adhesion,  given  in  the 
table  above,  have  received  specific 
names,  and  are  of  sufficient  impor- 
tance to  merit  separate  treatment: 
others  are  unimportant  in  every  re- 
spect. 

83.  Capillary  action.     If  a  clean 
glass  plate  is  placed  vertically  in  a 
basin  of  water,  the  liquid  will  rise 
on  each  side  to  the  height  of  nearly 
one-sixth  of  an  inch.     In  this  case, 

it  is  evident  that  the  force  of  adhesion  between  the  liquid 


Fio.  11. 


40 


NATURAL  PHILOSOPHY. 


and  the  solid  (III)  is  greater  than  the  cohesion  of  the  liquid 
molecules.  An  inspection  of  the  diagram  shows  that  any 
particle  of  the  glass  near  the  normal  surface  of  the  liquid 
can  have  no  influence  in  producing  this  elevation.  A  par- 
ticle at  d,  or  e  will  attract  the  upper  portion  of  the  liquid 
down  with  as  much  force  as  it  tends  to  raise  the  molecules 
beneath  it.  It  follows,  therefore,  that  the  whole  weight  of 
the  liquid  column  must  be  supported  by  the  narrow  line  of 
solid  particles,  6c,  near  the  top.  To  these  particles  the 
nearest  molecules  of  the  water  adhere,  and  support,  by  their 
cohesion,  the  second  line  of  molecules  of  water;  these,  in 
turn,  support  other  molecules,  and  so  on  until  the  weight  of 
the  column  equals  the  cohesion  of  the  upper  line  to  the 
second. 

84.  A  second  plate  of  glass  will  support 
an  equal  weight  of  the  liquid;  therefore, 
if  a  second  plate  be  placed  parallel  to  the 
first,  the  weight  of  the  water  supported 
will  be  double  that  of  a  single  plate.  If 
the  plates  are  brought  so  near  each  other 
that  both  plates  may  act  on  the  same 
molecules  of  the  liquid,  the  water  Avill  rise  between  the 
plates.  The  nearer  the  plates  the  higher  will  be  the  column 

of  water.  Two  plates,  one  hun- 
dredth of  an  inch  apart,  will 
support  a  column  of  water  two 
inches  high. 

85.  If  the  two  plates  are  in- 
clined toward  each  other,  and 
are  in  contact  at  one  vertical 

cil-c,  the  water  will  ri>e  Ix-tween 
them  to  heights  varying  in- 
\er~i-ly  as  the  distance  between 
the  plates.  The  outline  of  the 
surface  thus  formed  has  been  designated  the  equilateral  hy- 
perbola. 


FIG.  12. 


CAPILLARY   ATTRACTION. 


41 


86.  Finally,  if  the  molecules  of  the  liquid  are  attracted 
in  all  directions,  as  they  would  be  if  a  tube  were   substi- 
tuted for  the  glass  plate,  the  liquid  will  rise  to  twice  the 
height  produced   by  two   plates   separated   by   an   interval 
equal  to  the  diameter  of  the  tube.     A  tube,  one  hundredth 
of  an  inch  in  diameter,  will   support  a  column  of  water 
four  inches  high. 

87.  Because  these  phenomena  are  best  exhibited  in  tubes 
whose  internal  diameters  are  so  small  as  to  resemble  hairs, 
that  variety  of  adhesion  ivhich  causes  liquids  to  rise  on  solids  i# 
termed  Capillary  Attraction. 

The  height  to  which  a  liquid  will  rise,  varies  with  the 
nature  of  both  the  liquid  and  the  solid;  thus,  in  the  same 
glass  tube,  a  solution  of  carbonate  of  ammonia  will  rise 
a  little  higher  than  water;  nitric  acid  three-fourths,  and 
alcohol  a  little  more  than  one-half  as  high  as  water.  On 
the  other  hand,  mercury  will  not  wet  glass,  although  it  rises 
freely  on  lead,  zinc,  and  some  other  metals.  In  fact,  it 
may  be  demonstrated  that  liquids  will  not  rise  on  solids 
unless  the  adhesive  force  is  more  than  half  the  cohesive 
force.  Therefore,  although  mercury  is  attracted  by  glass, 
yet  as  this  attraction  is  less  than  twice  the  attraction  be- 
tween the  molecules  of  the  mercury,  the  phenomena  mani- 
fested when  glass  is  placed  in 
mercury  are  directly  opposite  to 
those  already  described  as  taking 
place  between  glass  and  water. 
The  most  satisfactory  experi- 
ments to  illustrate  capillary  ac- 
tion, are  conducted  in  glass  tubes 
of  the  shape  represented  in  Fig. 
14,  which  any  one  can  readily 
make  for  himself.  Water  poured 
into  A  assumes  a  concave  sur- 
face in  both  branches,  and  rises  FIG.  M. 
in  the  smaller  branch  above  the  level  of  the  larger.  Mer- 


B       B' 


4:2  NATURAL   PHILOSOPHY. 

cury,  poured  into  B,  assumes  a  convex  surface  in  both 
branches,  and  is  depressed  in  the  smaller  branch.  In  a 
greased  tube,  water  is  depressed.  A  needle,  slightly  greased, 
will  float  on  water,  because,  not  being  wet  by  the  liquid, 
it  produces  a  depression,  in  which  it  is  supported. 

88.  From  these  general  facts  it  is  easy  to  deduce  the  fol- 
lowing   laws    of   capillary  action,    when    applied    to    small 
tubes: 

1.  Liquids  ascend  in  tubes  when  they  wet  them,  and  are 
depressed  when  they  do  not. 

2.  The   ascent  and  depression   increase  as  the  diameters 
of  the  tubes  decrease. 

3.  The  ascent  and  depression  vary  with  the  nature  of  the 
substances  used. 

89.  Familiar  illustrations   of  capillary  attraction  are 
seen  in  the  action  of  the  wicks  of  lamps  and  candles.     If  one 
end  of  a  towel  is  plunged  in  a  basin  of  water  and  the  other 
end   is  left  hanging  over  the  edge,  the  whole  will   become 
wet.     Blotting  paper  is  useful  because  it  readily  draws  ink 
into  its  pores :  the  pores  of  letter  paper  are  closed  by  sizing. 
In  France,  dry  wooden  wedges  are  driven  into  holes  drilled 
in  rocks,  and  then  wet  with  water;  the  fibers  of  the  wood, 
by  absorbing  the  water,   expand  with  so  much  force  as  to 
split  the  rocks.     Water  can  not  be  poured  out  of  a  full 
tumbler  without  running  down  on  the  outside  of  the  glass, 
because  of  the  capillary  attraction. 

90.  Capillary  action    is   of  immense  importance   in    the 
operations  of  nature.     It  draws  the  water  necessary  to  the 
support  of  vegetation    to   the    surface   of  the    Around,    in 
the  drmi-hts  of  summer.     It  is  one  of  the  principal  causes 

«»f  I  he  ax-cnt  of  sap  in  plants,  and  plays  an  essential  part 
in  the  circulation  of  the  liquids  in  animal  tissues. 

91.  Solution.      If  a  lump  of  snirar  is  dipped  in  water,  the 
liquid  will  rise  by  capillary  attraction   until   the  whole  mass 


SOLUTION.  43 

is  moistened.  If  sufficient  water  be  present,  the  adhesion 
of  the  solid  to  the  liquid  (II)  will  be  sufficient  to  overcome 
the  cohesion  of  the  solid,  so  that  it  will  entirely  disappear 
in  the  liquid,  thereby  forming  a  solution.  Each  drop  of  the 
solution  has  the  sweetness  of  the  sugar  and  the  fluidity  of 
the  water,  thus  showing  that  the  adhesion  is  perfect,  because 
it  is  shared  by  every  molecule.  When  the  adhesive  force 
of  each  molecule  has  reached  its  limit,  no  more  of  the 
solid  will  dissolve,  and  the  solution  is  then  said  to  be 
saturated. 

92.  The   solvent    powers    of   liquids   vary   exceedingly. 
An   ounce  of  cold  water   can  dissolve   hardly  a  grain  of 
sulphate  of  lime,  although  it  readily  dissolves  one  thousand 
grains  of  sugar.     Many  substances  that  do  not  form  solu- 
tions  with   water    are    readily   dissolved   by   other   liquids. 
Water  is  the   best  general   solvent;    alcohol  is  the  proper 
solvent  for  resins;    ether  and  benzine,  for  fats;   bisulphide 
of  carbon,  for  sulphur  and  phosphorus;  mercury,  for  lead 
and  some  other  metals. 

The  solvent  powers  of  every  liquid  are  limited,  both  as  respects  the 
number  of  substances  soluble  in  it,  and  the  amount  of  any  one  neces- 
sary to  complete  saturation.  As  a  general  thing,  however,  when  a 
liquid  has  been  fully  saturated  with  one  solid,  it  is  still  capable  of 
dissolving  others. 

When  a  solid  disappears  in  an  acid,  as  copper  in  nitric  acid,  the 
action  is  twofold;  first,  a  chemical  action,  by  which  the  solid  and 
liquid  unite  to  form  a  substance  different  from  either,  as  nitrate  of 
copper;  second,  a  simple  solution,  by  which  the  compound  thus 
formed  is  dissolved  in  the  liquid. 

93.  The  adhesion  of  gases  to  liquids   (VIII)  is  illus- 
trated by  the  solution  of  gases  in  water  and  other  liquids. 
Water  dissolves  all  gases;  but  in  proportions  varying  (1.) 
with  the  nature  of  the  gas,  (2.)  the  temperature,  and  (3.) 
the  pressure.     The  following  table  shows  the  solubility  of 
several  of  the  gases  in  water    or  in  alcohol,  in  open  vessels 
and  at  the  freezing  point: 


44  NATURAL  PHILOSOPHY. 

Solubility  of  Gases. 

Volumes  of  gas  absorbed  by  one  volume 
of  water,  of  alcohol. 

Nitrogen  ..............................................       0.0204  0.12<i;; 

Oxygen  ................................................       0.0411  0.2840 

Carbonic  acid  ........................................       1.7967  -l.:;±i."> 

Sulphurous  arid  ....................................     68.8610  328.0200 

Hydrochloric  acid  .................................  506. 

Ammonia  .............................................  1049.7 

The  rapidity  with  which  water  absorbs  ammonia  may  be  prettily 
shown  by  the  following  experiment:  having  fitu-d 
a  glass  tube,  tapering  at  one  end,  to  the  cork  of  a 
large  bottle,  fill  the  bottle  with  dry  ammonia  gas. 
Then  invert  the  bottle,  and  place  the  mouth  of  the 
tube  in  water.  After  a  little  time  the  water  will 
absorb  so  much  of  the  ammonia  as  to  leave  a  par- 
tial vacuum  in  the  bottle;  the  external  pressure 
of  the  atmosphere  will  then  drive  the  liquid  up 
the  tube,  forming  a  fountain  of  greater  or  less 
force,  proportioned  to  the  size  of  the  upper  diam- 
eter of  the  tube. 

94.  The  weight  of  any  gas  absorbed  by 
Fl<1-  15-  a  liquid,   increases   directly  with    the   pres- 

sure; that  is,  if  the  pressure  is  doubled  or  tripled,  the 
weight  of  the  gas  absorbed  will  be  doubled  or  tripled.  It 
will  be  shown  hereafter  that  the  effect  of  pressure  on  a  <ras 
is  to  diminish  its  volume  and  increase  its  density,  in  pro- 
portion to  the  pressure.  For  this  reason,  the  volume  of 
the  gas  absorbed  is  the  same  for  all  pressures.  If  the  pres- 
sure is  removed,  the  gas,  by  virtue  of  its  elastic  force, 
resumes  its  original  density,  and  escapes  with  effervescence. 
The  soda  water  of  the  confectioner  is  water  charged  with 
carbonic  acid,  absorbed  under  pressure. 


95.  The  adhesion  of  gases  to  solids  (V}  is  governed  by 

nearly  tlie    >ame    laws   as   the    adhesion    of  liquids   to  solids 

111    .    with    tliis    important    difference,    that    .irases    are  very 

compre^ible.        When    water   is   heated    in    irluss   vosels,    the 

air  may  be  seen  to  leave  the  water  and  collect  in  bubbles 


ABSORPTION.  45 

on  the  side  of  the  vessel,  where  they  often  remain  for  some 
time.  Porous  solids,  as  meerschaum,  plaster  of  Paris, 
freshly  burned  charcoal,  and  metals  in  the  state  of  fine 
powder  often  absorb  large  amounts  of  gases.  The  follow- 
ing table  exhibits  the  number  of  volumes  of  several  of  the 
-uses  absorbed  by  one  volume  of  charcoal  and  of  meer- 
schaum : 

Absorption  of  Gases. 

Charcoal.        Meerschaum. 

Nitrogen 7.2  1.6 

Oxygen 9.2  1.49 

Carbonic  acid  35.  5.26 

Ammonia 90.  15. 

96.  A  piece  of  freshly  burned  charcoal,  exposed  to  the 
atmosphere  for  a  few  days,  will  often  increase  one-fifth  in 
weight.     This   phenomenon   can  be  explained  only  by  the 
supposition  that  the  solid,  by  reason  of  its  porous  condition, 
offers  a  very  large  extent  of  surface,   to  which  the  gases 
adhere   and  become   condensed.     Finely  divided   platinum 
absorbs  two  hundred  and  fifty  times  its  volume  of  oxygen. 
When  iron,  reduced  by  hydrogen,  is  poured  from  the  re- 
duction tube,  it  condenses  the  oxygen  of  the  air  so  rapidly 
that  the  iron  becomes  ignited. 

97.  The   absorptive   power   of  freshly  burned    charcoal 
is  of  great  economic  value.     The  variety  known   as  bone 
black  is  used  for  clarifying  sugars. 

The  brown  sirups  are  filtered  through  a  layer  of  this  charcoal  twelve 
or  fourteen  feet  in  thickness,  and  are  thus  obtained  perfectly  clear; 
all  the  coloring  matters,  whether  solid  or  liquid,  being  absorbed. 
Porter,  filtered  through  animal  charcoal,  loses  much  of  its  bitterness, 
and  all  of  its  gases.  All  varieties  of  charcoal  are  efficacious  in 
destroying  noxious  effluvia,  not  by  preventing  decay,  but  by  absorb- 
ing the  gaseous  products  of  decomposition. 

98.  Vesicular  condition.     In  clouds  and  fogs  the  moist- 
ure is  in  the  liquid  state,  and  is  supported  above  the  earth 
by  the  adhesion  of  liquids  to  gases  (VII). 


I',  NATURAL  PHILOSOPHY. 

It  has  been  supposed  that  each  drop  of  water  forms  a  vesicle  or 
bladder,  by  inclosing  a  molecule  of  air.  The  hollow  vesicle  exposes 
a  larger  surface  than  a  solid  drop  of  the  same  size,  and  continues  to 
float  until  the  drops  become  heavy  enough  to  overcome  the  adhesion 
of  the  air,  when  they  fall  as  mist  or  rain. 

99.  The  mechanical  transportation  of  dust,  snow,  and 
other  light  bodies  by  the  winds,  is  due  to  the  adhesion  of 
solids  to  gases  (IV).     Although  this  appears  to  be  a  trivial 
matter,  yet,  if  this  action  is  continued  for  a  long  series  of 
years,  it  affects  great  physical  changes,  as  is  seen  in  the 
dunes  of  France  and  England,   and  in   the  ever  shifting 
sands  of  the  deserts  of  Africa. 

DIFFUSION   OF   FLUIDS. 

100.  The  adhesion   of  liquids  to  liquids   (VI),   and  of 
gases  to  gases  (IX),  affords  phenomena  so  similar  that  they 
may  be  considered  together  under  the  general  theme  of  dif- 
fusion of  fluids. 

The  adhesion  of  some  liquids,  as  oil  and  water,  is  so 
feeble  that  they  can  not  be  made  to  unite  permanently  by 
any  amount  of  stirring  and  shaking.  On  the  other  hand, 
most  liquids  will  mix  readily  with  each  other,  though  in 
various  proportions ;  some,  as  water  and  alcohol  or  glycer- 
ine, are  miscible  in  all  proportions;  others  may  be  mixed 
only  to  a  limited  extent.  Thus,  if  water  and  ether  are 
shaken  together,  and  then  allowed  to  stand,  they  will,  in  a 
great  measure  separate,  each  liquid  dissolving  about  one 
tenth  (»f  the  other.  In  like  manner,  if  two  gases  which  do 
not  act  chemically  upon  each  other,  are  placed  in  the  same 
vessel,  they  will  form  a  permanent  mixture. 

101.  The  tendency  of  fluids  to  mix  with  each  other  is 
termed   Diffusion.     Diffusion   may  take  place   without   me- 
chanical  action,   and   even   in  apparent   opposition  to   the 
attraction  of  gravitation. 

Thus,  if  a  tall  jar  is  partially  filled  with  a  solution  of  blue  litmus, 
and  sulphuric  acid  is  poured  rnivfully  through  a  Imi.ij  funnel,  reach- 
ing to  the  bottom  of  the  jar,  the  line  of  separation  between  the  two 


DIFFUSION. 


47 


fluids  will  be  at  first  distinctly  marked.  This  will 
soon  disappear;  the  acid  will  gradually  rise  and  the 
water  will  sink  until  the  two  are  perfectly  mixed. 
This  will,  however,  require  some  time,  and  the  pro- 
gress of  diffusion  may  be  traced,  from  hour  to  hour, 
1)\-  watching  the  gradual  change  from  blue  to  red.  The 
experiment  may  be  repeated  with  almost  any  two 
liquids  of  different  specific  gravities,  as  alcohol  and 
water,  alcohol  and  turpentine,  or  the  saturated  solution 
of  any  salt  and  pure  water.  It  is  advisable  to  color 
one  of  the  liquids  with  a  little  cochineal  or  alkanet 
root.  The  rate  of  diffusion  will  be  found  to  vary  with 
the  nature  of  the  substances  used,  and  is  uniform  only 
in  dilute  solutions. 


FIG.  16. 


102.  The   diffusion   of  gases   may  be  illustrated  by  an 
apparatus    consisting  of  two    bottles, 

connected  by  a  long  glass  tube. 

Fill  the  upper  with  the  lighter  gas,  as 
hydrogen,  and  the  lower  with  a  heavier,  as 
chlorine.  In  the  course  of  two  or  three 
hours  the  two  will  mix  perfectly  and  per- 
manently. The  green  color  of  the  chlorine 
enables  us  to  trace  its  gradual  ascent.  This 
experiment  should  be  performed  only  in 
diffused  daylight,  or  in  a  darkened  room,  to 
avoid  an  explosion.  The  experiment  may 
be  modified  by  filling  two  jars  over  a  pneu- 
matic trough,  one  half  full  of  hydrogen,  the 
other  half  full  of  air,  so  that  the  water  shall 
stand  at  the  same  level  in  both.  If,  now, 
we  pass  a  few  drops  of  ether  into  each  jar, 
the  same  quantity  of  ether  will  evaporate  in 
both,  and  ultimately  cause  the  same  depres- 
sion of  water  level,  but  the  diffusion  will  be 
much  more  rapid  in  the  hydrogen. 

103.  The    diffusion    of  gases    is   of 

the  greatest  importance  in  maintaining  the  purity  of  the 
atmosphere.  The  constituents  of  the  air  are  of  different 
specific  gravities,  and  would  arrange  themselves  with  the 
heaviest  at  the  bottom,  were  it  not  for  this  beneficent  law  of 


48 


NA  T URA L  miL 0 SOPHY. 


nature.  The  noxious  products  of  combustion  and  decay 
would  then  be  found  at  the  surface  of  the  earth,  and  would 
produce  the  most  disastrous  consequences.  As  it  is,  they  arc 
rapidly  diluted  when  formed,  and  soon  are  so  perfectly  dis- 
seminated through  the  atmosphere,  that  the  most  accurate 
chemical  analysis  fails  to  find  any  essential  difference  in  the 
air  of  mountain,  plain,  or  valley. 

104.  Osmose.      The   diffusion   of   fluids   may   take  place 
when   they  are  separated  by  a  porous  partition  or  septum. 

Inasmuch  as  the  phenomena 
are  greatly  modified  by  the 
presence  of  the  septum,  the 
diffusion  of  fluids  through 
septa  has  been  termed  osmose. 

Tie  a  long  glass  tube  to  the 
mouth  of  a  membranous  bag  or  a 
bladder.  Fill  the  bag  with  strong 
brine,  sirup,  or  alcohol,  and  then 
immerse  it  in  pure  water.  After 
a  while  it  will  be  found  that  the 
liquid  has  risen  in  the  tube,  and 
that  the  outer  vessel  contains  some 
of  the  liquid  which  was  in  the  in- 
terior. Hence,  a  current  has  been 
produced  in  two  directions.  The 
one  passing  to  the  liquid  which 
increases  in  volume  is  called  end- 
osmose,  the  other  is  called  erosmose. 
The  rate  of  diffusion,  and  (he  vol- 
ume of  water  diffused,  is  greater 
in  osmose  than  in  simple  diffusion. 


FIG.  18. 


The  cause  of  osmose  has  not  been  clearly  explained,  but 
the  conditions  of  its  action  seem  to  Itc: 

1.  That   the  liquids  he  capable  of  mixing. 

2.  That     the    septum     have    a    L:reatcr    adhesion    for    one 
liquid  than   the  other. 

Experiments  in  osmose  may  be  conducted  by  using,  in- 


DIALYSIS. 


49 


stead  of  the  bag  in  Fig.  18,  an  inverted  funnel,  having  its 
mouth  closed  by  a  strip  of  any  animal  membrane,  or  by 
parchment  paper. 

105.  Dialysis  is  the  application  of  osmose  to  the  separa- 
tion of  the  constituents  of  a  liquid.     Alcohol,  hydrochloric 
acid,  and  substances  capable  of  forming  crystals,  when  in  a 
state  of  solution,  readily  pass  through  septa.     On  the  other 
hand,  gelatine,  gum  arabic,  and  other  substances  that  do 
not  crystallize,  do  not  exhibit  this  property.     Hence,  if  a 
solution  contain   crystallizable   and   gelatinous   substances, 
the  former  will  suffer  osmosis,  and  the  latter  will  remain 
above  the  septum. 

106.  The  osmose  of  gases  may  be  shown  by  a  striking 
experiment : 

Take  a  glass  funnel  with  a  long 
delivery  tube.  Close  its  mouth  by  a 
septum  of  plaster  of  Paris.  This  may 
be  done  by  making  a  moderately  thick 
paste  of  the  plaster  with  water  on  a 
plate,  inverting  the  mouth  of  the  fun- 
nel therein,  and  then  suffering  the 
plaster  to  harden,  and  to  dry  thor- 
oughly. Now  attach  the  open  end  to 
a  flask  containing  water  and  fitted 
with  a  jet  pipe  extending  beneath  the 
water,  as  in  Fig.  19,  and  invert  over 
the  septum  a  jar  filled  with  hydrogen. 
The  endosmose  of  the  hydrogen  will 
be  so  rapid  as  to  force  out  the  water 
from  the  jet  tube  in  a  miniature 
fountain.  Remove  the  jar,  and  air 
will  bubble  through  the  water,  show- 
ing the  escape  of  the  hydrogen  through 
the  septum. 

Fig.  19. 

India  rubber  balloons,  filled  with   hydrogen,  soon  become 
flaccid,  from  the  escape  of  the   hydrogen  into   the  air, 
N.  P.  4. 


50  NATURAL   PHILOSOPHY. 

107.  Although  the  nature  of  osmose  can  not  be  satis- 
factorily determined,  it  is  manifest,  from  the  porous  nature 
of  vegetable  and  animal  membranes,  that  it  must  play  an 
important  part  in  the  operations  of  life.  We  know  that 
poisons  may  be  absorbed  through  the  skin.  It  is  probable 
that  the  ascent  of  sap  in  plants,  and  the  various  processes 
of  secretion  in  animals,  are  either  controlled  or  essentially 
modified  by  osmotic  action. 

108.  Recapitulation. 

The  varieties  of  adhesion  are : 
I. 

Solids  to  solids J  Cements, 

<•  Friction. 
III. 

Liquids  to  solids f  Capillarity, 

<>  Filtration. 
II. 
Solids  to  liquids Solution  of  solids- 

VIII. 
Gases  to  liquids Solution  of  gases. 

V. 

Gases  to  solids Absorption  of  gases. 

VII. 

Liquids  to  gases Vesicular  condition- 

IV. 
Solids  to  gases Sand  hills. 

VI. 

Liquids  to  liquids Diffusion  of  liquids. 

IX. 

Gases  to  gases Diffusion  of  gases. 

Osmose Diffusion  through  septa- 


MECHANICS.  51 


CHAPTER    III. 


109.  It   has   been   shown   that   motion   is  caused  by  the 
action  of  force  upon  matter;    but  we  can   readily  conceive 
that  two  or  more  forces  may  so  act  upon  a  body  that  their 
effects  will    mutually  counteract    each   other,  and   that  no 
motion  will  ensue.     In  this  case,  the  forces  are  said  to  be  in 
equilibrium,  and  the  body  is  said  to  be  at  rest. 

110.  Mechanics  is  the  science  which  treats  of  equilibrium 
and  motion.     That  part  of  it  which  relates  to  equilibrium 
is  called  Statics,  and  that  which  relates  to  motion  is  called 
Dynamics.      In    the    present   treatise,    no   attempt  will    be 
made   to   separate  statical   and  dynamical   propositions,   as 
the  study  of  either  presupposes  the  student  to  have  some 
knowledge  of  the  other.     As  a  general  rule,  the  facts  in 
dynamics  will  be  considered  last. 

111.  Inasmuch  as  mechanics  relates  to  all  bodies,  whether 
solid,  liquid,  or  aeriform,  it  has  been  found  convenient  to 
divide  the  science  into  three  divisions: 

1.  The  mechanics  of  solids,  called  statics  and  dynamics. 

2.  The  mechanics  of  liquids,  called  hydrostatics  and  hydro- 
dynamics. 

3.  The   mechanics   of  gases,   called  pneumatics,   or  aero- 
statics, and  aerodynamics. 

GENERAL   STATICS    AND    DYNAMICS. 

112.  The  forces  considered  in  mechanics  may  be  reduced 
to  gravity,  elasticity,  and  muscular  strength. 

If  a  force  acts  but  for  an  instant,  it  is  called  an  impulsive. 
force.  If  its  action  is  continued,  it  is  called  an  incessant, 
or  continuous  force.  A  continuous  force  may  be  regarded  as 


52  NATUllAL   PHILOSOPHY. 

a  series  of  impulsive  forces,  acting  in  exceedingly  brief  but 
equal  units  of  time.  If  the  impulses  are  equal  in  intensity, 
it  is  called  a  constant  force;  but  if  their  intensity  changes, 
it  is  called  a  variable  force. 

113.  Since  motion  is  produced  by  the  action  of  force 
upon  matter,  it  must  vary  with  the  kind  of  force  producing 
it.  An  impulsive  force  produces  -uniform  motion  —  a  contin- 
uous force  acting  alone  produces  varifd  motion. 

I.  UNIFOK.M    MOTION    is  that    in  which    equal  spaces  are 
described   in    equal    times.     A    body    once   set    in    motion, 
would,  by  virtue  of  its  inertia,  continue  moving  in  a  straight 
line  with    uniform  velocity  forever,  were  there  no  opposing 
forces.     But  as  every  moving   body  meets  with  resistances, 
such  as    gravity    and    friction,  it  must   soon    be   brought  to 
rest  unless  impelled  by  a  continuous  force. 

Continuous  forces  may  produce  uniform  motion  when 
the  successive  impulses  are  exactly  equal  to  the  resistance. 
Thus,  a  railway  train  moves  with  uniform  velocity  when 
the  friction  and  the  resistance  of  the  air  have  increased  so 
as  to  be  in  equilibrium  with  the  motive  power  of  the  en- 
gine. 

Thus,  also,  the  earth  revolves  on  its  axis,  in  exactly  uni- 
form motion.  The  time  of  one  revolution  is  divided  into 
86,400  equal  parts,  one  of  which  is  called  a  second,  and 
constitutes  the  unit  of  timr. 

Tlie  velocity  of  a  body  is  the  space  described  in  a  unit  of 
time. 

II.  VARIED  MOTION  is  that  in  which  unequal  spaces  are 
described    in    equal    successive    units    of   time.     If   a   body 
describes  a  greater    space    in    each    successive    moment,  the 
motion   is  acn  l>  r»t«l;  but  if  the  space  is  less,  the  motion  is 
retarded. 

A  constant  fon-r  acting  alone  upon  a   body   will    produce 
accelerated  motion. 


\  falling  Ixxly  may  l>e  taken  ;i<  :m  example  of  this  kind  of  motion. 
Tlu-   moment    it    is   Unsupported,  gravity  causes    it    to  defend,  suul   if 


MOMKXTL'M.  53 

this  force,  and  all  opposing  forces,  were  then  annihilated,  it  would 
fall  with  uniform  motion;  but  gravity  continues  to  act  with  new  im- 
pulses at  each  moment,  and  thus  forces  the  body  downward  faster 
and  faster.  This  illustration  is  not  perfect,  because  the  resistance  of 
tlu-  air  increases  as  the  square  of  the  velocity  of  the  body,  and,  if  the 
body  continues  long  in  falling,  will  at  last  produce  uniform  motion. 

A  constant  force  opposing  the  previous  motion  of  a 
body  produces  uniformly  retarded  motion.  Thus,  when  a 
body  is  thrown  vertically  upward,  gravity  retards  its  motion 
every  instant  and  will  finally  bring  it  to  rest. 

The  velocity  in  uniformly  varied  motion,  at  any  moment,  is  ike 
space  a  body  would  describe,  by  lirtue  of  its  inertia,  in  Hie  next 
subsequent  unit  of  time,  were  all  forces  acting  upon  it  to  cease. 

114.  Momentum.  When  a  body  is  in  motion,  the  effect 
may  be  measured  by  the  time  that  would  be  required  to 
stop  the  motion  by  a  pressure  of  uniform  intensity.  This 
pressure,  multiplied  by  the  time  througli  which  it  acts,  is 
equal  to  the  mass  of  the  body  mmltiplied  by  its  velocity. 
This  last  product  is  the  momentum  of  a  body,  or,  as  it  is 
sometimes  called,  its  quantity  of  motion. 

Of  two  equal  masses,  that  which  has  the  greater  velocity 
will  have  the  greater  momentem;  of  two  unequal  masses, 
having  the  same  velocity,  the  heavier  mass  will  have  the 
greater  momentum.  The  momentum  is,  therefore,  depend- 
ent on  the  weight  and  the  velocity,  and  may  be  estimated 
by  the  following  rule:  the  momentum  is  equal  to  the 
weight  multiplied  by  the  velocity. 

[5.]  M  =  WXV. 

The  momentum  of  a  thirty  pound  cannon  ball,  moving  with  a 
velocity  of  one  thousand  feet  per  second,  is  equal  to  thirty  thousand 
pounds — that  i<,  it  is  equal  to  the  momentum  of  a  body  weighing 
thirty  thousand  pounds  and  moving  one  foot  per  second.  From  these 
considerations  it  is  evident  that  the  momentum  of  a  large  body  mov- 
ing slowly  may  be  no  greater  than  that  of  a  small  body  moving 
rapidly.  Thus,  the  momentum  of  an  enormous  but  slow  sailing  ship 
may  be  no  greater  than  that  of  a  swift  steam  tug.  The  momenta  of 
very  large  masses,  as  icebergs,  are  irresistible  by  any  human  power, 
even  though  their  motion  be  so  slow  as  to  be  almost  imperceptible. 


54  NATURAL  PHILOSOPHY. 

LAWS    OF   MOTION. 

115.  The  deductions  in  mechanics  are  based  upon  three 
axioms,  known  as  Newton's  laws  of  motion. 

FIRST  LAW.  —  Every  body  continues  in  a  state  of  rest,  or  of 
uniform  motion  in  a  straight  line,  unless  acted  on  by  some  ex- 
ternal force. 

This  is  called  the  law  of  inertia,  because  it  depends  on  that  property 
of  matter.  It  is  difficult  to  furnish  examples  which  will  perfectly  illus- 
trate this  law,  because  all  bodies  on  the  earth  are  constantly  acted  on 
by  one  or  more  external  forces.  The  following  are  given  as  approxi- 
mate illustrations: 

That  a  body  can  not  set  itself  in  motion  is  evident  from  our  expe- 
rience. Mountain  cliffs  remain  for  ages,  until  worn  away  by  winds, 
rain,  frost,  or  other  agencies. 

That  a  body  tends  to  move  in  a  straight  line  may  be  seen  by  roll- 
ing a  ball  along  the  ground,  or  on  the  floor,  or  on  a  smooth  sheet  of 
ice;  the  fewer  the  obstacles  in  the  way,  the  more  direct  will  be  its 
course.  The  same  experiment  shows  that  the  fewer  the  obstacles,  the 
more  uniform  will  be  the  rate  of  motion,  and  the  longer  will  it  con- 
tinue in  motion. 

116.  Whatever  tends  to  oppose  or  retard  motion  is  called 
the  Resistance.     The  resistances  which  a  moving  body  en- 
counters  are,  mainly,  gravity,  friction,  and   the   resistance 
of  the  medium  surrounding  it,  as  air  or  water. 

There  are  some  apparent  exceptions  to  the  law  of  inertia.  A  heavy 
ring  may  be  so  struck  by  the  hand  that  it  will  proceed  a  little  dis- 
tance, on  a  level  surface,  and  then  return  to  the  hand.  In  this  eas.-, 
the  hand  not  merely  gives  the  ring  an  impulse  forward,  but  imparts 
a  rotary  motion  in  the  opposite  direction.  The  rotary  motion  soon 
destroys  the  impulse  forward,  and  causes  the  body  to  change  its 
direction. 


117.  SECOND  LAW.  —  Mnflnn,  <>/•  «  <-!i<ni</<'  <>f  iimfiun,  it  pro- 
portional to  the  force  impressed,  and  is  in  the  direction  of  the 
line  in  which  that  force  acts. 

In  order  to  comprehend  the  action  of  a  force,  throe  things 
must  lie  known:  M.)  its  intensity,  (2.)  its  direction,  (3.) 
its  point  of  application. 


MOTION.  55 

1.  The  intensity  of  a  force  is  the  energy  with  which  it 
acts.     This  may  be  expressed  in  pounds,  and  may  be  repre- 
sented by  a  straight  line.     Thus  if  we  represent  a  force  of 
one  pound  by  a  line  an  inch  long,  any  multiple   of  the 
force  will  be  expressed  by  a  line  of  corresponding  length. 

2.  The  direction  of  a  force  is  the  line  along  which  it  acts. 

3.  The  point  of  application  of  a  force  is  the  point  upon 
which  it  exerts  its  action. 

118.  If  a  given  force  generates  a  given  motion,  a  double 
force  will  generate  double  the  motion.     It  must  not  be  sup- 
posed  that    twice   the   velocity   will   actually  be    realized. 
Thus,  if  an  engine  can  propel   a   steamboat  ten  miles  an 
hour,  two   engines  of  the  same  power  will  not  double  its 
speed,  because  the  resistance  of  the  water  increases  as  the 
square  of  the  velocity. 

119.  A  body  may  be  acted  upon  by  a  single  force,  or  by 
several  forces  at  the  same  time.     By  the  terms  of  the  second 
law,  each  will  produce  the  same  effect  as  if  it  acted  alone. 
Motions    are,    therefore,    classified,    with    reference    to    the 
number  of  forces  employed,  as  simple  and  compound. 

120.  Simple  motion  is  produced  by  the  action  of  a  single 
force. 

Compound  motion  is  produced  by  the  joint  action  of  two 
or  more  forces.  The  following  are  selected  from  the  many 
cases  that  may  occur : 

CASE  I.  If  several  forces  act  upon  the  same  point  in  the 
same  direction,  their  effect  will  equal  their  sum. 

Thus,  if  a  carriage  be  drawn  by  two  horses,  one  exerting  a  force 
of  two  hundred  pounds,  and  the  other  three  hundred  pounds,  then 
their  combined  effect  will  be  the  same  as  that  of  a  single  horse  pull- 
ing with  a  force  of  five  hundred  pounds. 

A  single  force  that  represents  the  effect  of  several  forces 
acting  together,  is  called  their  resultant.  The  forces  which 
combine  to  make  up  the  resultant  are  called  its  components. 


56 


NATURAL  PHILOSOPHY. 


When  these  forces  produce  motion,  the  sum  of  the  velocities  of 
the  components  will  equal  the  velocity  of  the  resultant.  Thus,  if 
a  boat,  impelled  on  quiet  water  by  oars  at  a  rate  of  four  miles  an 
hour,  enters  a  river,  flowing  in  the  same  direction  at  a  rate  of  three 
miles  an  hour,  the  speed  of  the  boat  will  become  seven  miles  an  hour. 

121.  CASE  II.  If   two  forces   act   upon    the    same    point 
in  opposite  directions,  their  resultant  equals  their  difference. 

If  the  carriage  be  drawn  forward  with  a  force  of  three  hundred 
pounds  and  backward  with  a  force  of  two  hundred  pounds,  an  effect 
of  one  hundred  pounds  will  remain  in  the  direction  of  the  greater 
force.  If,  in  the  previous  example,  the  boat  proceed  up  the  river 
against  the  current,  it  will  have  a  velocity  of  one  mile  per  hour  in  the 
original  direction. 

122.  CASE  III.  If  two  forces  which  act  upon  the  same 
point   are   represented    in   intensity   and   direction    by   the 

adjacent  sides  of  a  parallelogram,  the  diag- 
onal will  represent  their  resultant  in  in- 
tensity and  direction. 

Suppose  a  boat  to  be  rowed  at  the  rate  of  four 
miles  an    hour,    in    the   direction    A  B,   across    a 
stream   running   at  three   miles   an   hour,  in  the 
direction  AC.     The  boat  will  move  in  the  direc- 
tion A  D,  the  resultant  of  these  components,  at 
the  rate  of  five  miles  an  hour. 

This  proposition  is  called  the  parallelogram  of  forces,  and 
the  operation  of  finding  the  resultant  when  the  components 
are  given  is  called  the  composition 
of  forces.  When  the  forces  are  at 
right  angles  to  each  other,  the  find- 
ing of  the  resultant  is  an  easy  geo- 
metrical problem  of  finding  the  hy- 
potenuse when  the  two  sides  are 
given.  Many  familiar  natural  phe- 
nomena may  be  explained  by  this 
principle. 

A  bird,  in  flying,  beats  the  air  with  wings 
inclined  toward  each  other.     The  resistance  t.f  the.  air  is  perpendicular 


Fio.  21. 


MOTION. 


57 


to  their  surfaces.  Draw  A  F  and  A  G  perpendicular  to  each  wing,  and 
lay  off  on  them  A  E  and  A  D,  to  represent  the  force  of  each  wing. 
Now  complete  the  parallelogram  A  E  C  D,  and  draw  its  diagonal  A  C. 
This  will  be  the  resultant  of  the  two  forces,  and  the  bird  will  move 
as  if  impelled  by  the  single  force  A  C. 

A  bullet  dropped  from  the  topmast  of  a  ship  in  rapid  motion, 
will  strike  the  deck  precisely  where  it  would  have  fallen  had  the 
vessel  been  at  rest.  The  reason  of  this  is,  that  the  ball,  which  falls 
by  the  action  of  gravity,  also  partakes  of  the  motion  of  the  vessel, 
which  carries  it  forward  as  fast  as  the  ship  moves. 

123.  Conversely,  when  the  resultant  of  two  forces  is 
given,  the  components  equivalent  to  it  may  be  found.  This 
operation  is  called  the  resolution  of  forces. 

Represent  any  force,  equal  in  C 

intensity  to  ten,  by  the  line  A  C. 
On  this  line  an  infinite  number 
of  parallelograms,  ABC  B', 
ADCD',  AECE',  may  be 
constructed,  any  two  adjacent 
sides  of  which  may  be  considered 
as  the  components  of  A  C.  Thus, 
if  A  B  be  drawn  equal  in  intensity  to  eight,  A  Bx  at  right  angles  to  it 
will  equal  6. 


— -xE 


As  an  illustration,  take  the  sailing  of  a  sloop  under  a  wind  oblique 
to  the  course  of  the  boat.     Represent  the  course  of  the  wind  by  the 


58 


NATURAL  PHILOSOPHY. 


R 


line  V  m.  Its  force  may  be  resolved  into  two  components ;  the  one  t  tf, 
tangent  to  the  sail,  and  producing  no  effect,  the  other,  m  n,  per- 
pendicular to  the  sail.  As  the  sail  is  oblique  to  the  axis  of  the  boat, 
this  force  will  tend  to  give  the  boat  a  lateral  motion,  called  the  lee- 
way. Therefore,  _this  force  is  again  decomposed  by  the  keel  and  the 
rudder,  and  the  useful  component  impels  the  sloop  on  its  course. 

124.  CASE  IV.  When  more  than  two  forces  act  upon  the 
same  point,  the  final  resultant  may  be  found  by  combining 
any  two  for  the  first  resultant,  then  a  third  force  with  the 
first  resultant,  then  a  fourth  force  with  the  second  resultant, 
and  so  on,  until  all  the  forces  have  been  combined. 

Thus,  in  Fig.  24,  Ar  is  the  re- 
sultant of  AB  and  AC;  A?y  the 
resultant  of  A  r  and  AD;  A  R  the 
resultant  of  A  r7  and  A  E,  and,  con- 
sequently the  resultant  of  the  four 
forces,  A  B,  A  C,  A  D,  and  AE. 

125.  CASE  V.  When  two 
parallel  forces  act  upon  a  line, 
B  C,  their  resultant  will  also 
be  parallel,  and  will  have  its  point  of  application  at  a 
distance  from  either  force,  inversely 
proportional  to  its  intensity.  If 
the  forces  lie  in  the  same  direction, 
the  resultant  will  equal  their  sum, 
as  in  the  case  of  horses  attached  to 
the  same  whippletree.  If  the  forces 
F  and  F'  lie  in  opposite  directions, 
as  in  Fig.  25,  the  resultant  F— F' 
will  equal  their  difference,  and  lie 
in  the  direction  of  the  greater  force. 

When  opposite  parallel  forces  are  equal,  they  produce  no 
progressive  motion,  hut  cause  the  body  on  which  they  act 
to  revolve  aliotit  a  point  midway  between  the  two  forces. 
Such  a  >\>tem  is  called  a  counle. 

By  the  application  of  these  principles,  an  approximate  answer 
may  be  obtained  lor  problems  who.se  accurate  solution  requires  the 


FIG.  24. 


FIG.  25. 


ACTION  AND  REACTION. 


59 


FIG.  26. 


higher  mathematics.  Thus,  suppose  a  known  vertical  force,  acting 
upon  the  point  L,  to  be  resists!  l»y  two  forces,  acting  on  each  side 
of  it,  at  angles  respectively  forty  and  thirty  degrees,  and  suppose 
the  value  of  these  components  to  be  required.  Represent  these  forces 
by  the  lines  L  G,  L  X,  L  E,  and  set  off  on  LG  the  value  of  the 
vertical  force,  in  any  convenient  unit,  as 
one  inch,  or  one  foot.  Through  G,  draw 
lines  so  as  to  complete  the  parallelogram. 
The  sides  of  the  parallelogram  L  X  and 
L  E  will  be  the  forces  required,  and  their 
lengths,  measured  by  a  scale  of  equal 
parts,  will  give  their  ratio  to  each  other, 
and  to  the  known  force  L  G.  This  is 
the  method  by  construction.  In  the  case 
supposed  LG  =  1,  LE  =  0.67,  LN  =  0.52, 
an  answer  correct  to  two  places  of  deci- 
mals. Conversely,  had  L  E  and  L  X  been 
known,  their  resultant,  L  G,  equals  the 
force  necessary  to  counteract  them,  or 
1.00. 

126.  THIRD  LAW. — Action  and  reaction  are  always   equal, 
and  are  in  opposite  directions. 

A  weight,  suspended  from  a  hook,  is  retained  in  its  place  because 
the  hook  reacts  with  a  force  equal  to  the  pull  of  the  weight.  When 
a  ball  is  fired  from  a  cannon,  the  cannon  recoils  with  a  momentum 
equal  to  that  of  the  ball,  but  the  backward  motion  is  much  less 
because  of  the  greater  weight  of  the  cannon.  A  rocket  rises  from 
the  reaction  of  the  air  against  its  expanding  gases.  A  bird,  in  flying, 
beats  the  air  with  its  wings,  and  by  giving  a  stroke  whose  reaction 
is  greater  than  the  weight  of  its  body,  rises  with  the  difference. 
When  a  pugilist  strikes  his  antagonist,  his  fist  sustains  as  great  a 
shock  as  it  gives,  but  is  usually  less  sensitive  to  injury  than  the  part 
on  which  it  strikes. 

127.  When    a    moving   body   encounters    another,    the 
effects  of  action  and  reaction  are  modified  by  elasticity,  and 
other  circumstances.     The  reaction  of  solids  may  be  shown 
by  balls  of  different  material  and  size,  hung  from  a  frame, 
so  that  their  diameters  shall  lie  in  the  same  straight  line. 

128.  Non-elastic   solids.     If  two   balls,    of  soft  wax   or 
clay,  be  suspended,  and  one  be  let  fall  upon  the  other  at 


60 


NA  T  URA  L    PHIL  OSOPIIY. 


rest,  the  first  will  communicate  a  part  of  its  momentum  to 
the  second,  and  both  will  move  forward  with  the  original 

momentum.  The  velocity 
of  the  two  will  be  dimin- 
ished in  proportion  as  their 
combined  weight  exceeds 
that  of  the  falling  ball. 

If  both  are  dropped  to- 
ward each  other,  they  will 
come  to  rest,  on  striking, 
if  their  momenta  are 
equal.  This  will  be  the 
case  if  equal  balls  are 
dropped  with  equal  veloc- 
ities. If  their  momenta. 
are  unequal,  they  will 
move,  after  collision,  in 
the  direction  of  the  greater, 
and  with  a  momentum 
equal  to  the  difference  of 
the  original  momenta. 

129.  Elastic  bodies.  In  perfectly  elastic  bodies,  the  force 
of  elasticity  is  exactly  equal  to  that  of  compression,  and  in 
such  bodies  the  effect  of  reaction  is  of  the  same  kind  as 
that  of  action. 

Suspend  two  equal  ivory  balls  from  the  frame  in  Fig. 
27.  If  b  falls  upon  &',  it  will  lose  half  its  velocity  in  com- 
pressing &',  and  the  body  b'  will  destroy  an  c<jii:il  amount 
in  regaining  its  shape;  therefore,  b  will  lose  all  its  velocity, 
and  remain  at  rest.  By  the  same  process  of  reasoning,  b' 
will  acquire  all  the  velocity  of  />,  and  would  rise  as  far  a>  /> 
fell,  were  it  not  for  the  want  of  perfect  elasticity. 

If  the  two  balls  are  dropped  with  unequal  velocity,  in 
the  same  direrti.m,  each  will  move,  after  colli>i<.n,  with  the 
previous  velocity  of  the  other  body.  For,  as  before,  bf 
gains  what  b  loses. 


COLLlSHty   OF  BODIES.  61 

If  the  balls  collide  from  opposite  directions,  each  will 
rebound  with  the  previous  velocity  of  the  other  body. 

130.  Bodies  striking    a  fixed    plane.      Let  a  ball   be 

thrown  in  the  direction  I  N, 
upon  a  hard  and  smooth  plane 
A  B,  and  suppose  both  bodies 
to  be  perfectly  elastic.  The 
force  of  the  collision  at  N, 

may  be  resolved  into  two  com-      ..  |JV  K 

ponents;  the  one,  N  D,  perpen- 
dicular to  A  B,  which  repre- 
sents the  elastic  force,  tending 
to  urge  the  ball  in  the  line 

N  P,  and  the  other  component,  N  E,  parallel  to  A  B,  repre- 
senting its  velocity  in  the  direction  of  the  plane.  Complete 
the  parallelogram,  NERG,  its  diagonal,  N  R,  will  repre- 
sent the  direction  the  ball  will  take  after  impact.  A  careful 
measurement  will  show  that  the  angle,  I  N  P,  is  equal  to 
the  angle  PNR. 

The  angle,  INP,  formed  by  the  direction  of  the  inci- 
dent body  and  the  perpendicular,  is  called  the  angle  of  inci- 
dence, and  the  angle,  P  N  R,  formed  by  the  perpendicular 
and  the  direction  of  the  body  after  reflection,  is  called  the 
angle  of  reflection.  Their  equality  is  expressed  by  the 
following  law:  The  angle  of  incidence  is  always  equal  to  the 
angle  of  reflection. 

This  law  applies  exactly  to  the  reflection  of  sound,  light, 
and  heat,  and  of  perfectly  elastic  bodies. 

If  either  body  is  imperfectly  elastic,  the  component,  N  G, 
will  be  proportionally  smaller;  hence,  the  body  will  pro- 
ceed, after  reflection,  in  a  line  nearer  the  plane  than  N  R, 
and  the  angle  of  reflection  will  be  greater  than  the  angle 
of  incidence. 

These  facts  may  be  readily  exemplified  by  bounding  balls  of  differ- 
ent elasticities,  as  rubber,  ivory,  marble,  clay,  putty,  etc.,  upon  a  hard 
floor,  and  are  well  shown  in  the  game  of  billiards. 


62  NATURAL   PHILOSOPHY. 

131.  Reaction  in  soft  bodies.     In  the  previous  cases,  the 
reaction  has  been  supposed  to  be  instantaneous,  but  if  the 
reaction  is  gradual,  its  destructive  effect  will  be  less. 

Thus,  if  a  man  leaps  from  a  height  into  deep  water,  the  particles  of 
the  water  separate,  and,  though  the  reaction  is  the  same  as  though  he 
alighted  on  a  solid  plane,  it  is  diffused  through  a  sufficient  interval 
of  time  to  become  comparatively  harmless.  In  like  inamuT  stones 
may  be  caught  in  the  hand  with  impunity,  if  the  hand  is  allowed  for 
a  time  to  partake  of  the  motion  of  the  stone. 

132.  Even  soft  bodies  require  some  time  for  the  displace- 
ment of  their  particles.     If  the  surface  of  water  be   struck 
sharply  by   the  open  palm,  the  blow  is  resisted  almost  as 
well  as  by  solids.     This  power  of  resistance  for  the  moment 
is  exemplified   by  the  sport  of  ''skipping  stones"  along  the 
surface  of  smooth  water.     Leaden  bullets  will   become   flat- 
tened if  fired  obliquely  upon  water. 

133.  Diffused  action.     If  a   blow  be  struck  on  a  large 
body,  the  effect  on  each  particle  will  be  inversely  propor- 
tional to  the  mass.     Thus,  if  an  anvil  be  laid  on  the  chest 
of  a  man,  he  may  receive  a  heavy  blow  on  it  without  detri- 
ment, because  the  blow  is  first  diffused  through  the  anvil, 
and  then  deadened  by  the  expanded  lungs  of  the  man. 

134.  Striking  force.     In  these  examples,  bodies  have  been 
considered   as   under   the    influence   of   momentum,    which 
expresses  the  intensity  of  the  moving  force.     The  energy  of 
a  force  is  its  power  to  perform  work,  that  is  to  overcome 
resistance  through   a  certain   space.     This  is  called  the  vis 
viva,  or  striking  force. 

Thus,  the  momenta  of  two  balls,  weighing  five  and  ten  pounds,  will 
he  the  same  if  the  lighter  hall  moves  with  twice  (lie  velocity  of  the 
heavier;  hut  if  both  strike  a  clay  hank,  the  swifter  hall  will  penetrate 
twice  as  far  a-  the  other,  or  perform  doiihle  the  work.  This  differ- 
ence is  due  to  their  striking  force. 

135.  Either  momentum  or  vis  viva  may  be  taken  as  the 

measure  of  a  force.      The    iiioninifinii    ivprr.-enN    thr   amount 
of  pressure  which,  if  applied   to  a  moving  body  for  one  sec- 


COLLISION.  63 

ond,  will  bring  the  body  to  rest.  With  a  given  mass,  the 
momentum  is  proportional  to  the  velocity  of  the  body.  The 
vis  viva  represents  the  energy  required  to  keep  a  body  in 
motion  with  a  constant  velocity.  Suppose  a  locomotive  to 
double  its  velocity :  it  encounters  twice  as  many  points  of 
resistance,  and  strikes  each  of  these  with  double  velocity; 
hence,  to  maintain  a  double  velocity,  its  energy  of  motion 
must  be  increased  four  times.  If  it  trebles  its  velocity,  its 
energy  must  be  increased  nine  times,  etc.  That  is,  with  a 
given  mass  the  vis  viva  is  proportional  to  the  square  of  the 
velocity.  The  work  which  a  moving  body  can  do  through 
a  certain  space  before  it  is  brought  to  rest  is  the  measure 
of  its  energy  at  any  moment.  Its  average  velocity  will 
be  only  one-half  of  the  initial  velocity,  and,  hence,  The  vis 
viva  equals  one-half  of  the  product  of  the  mass  multiplied  by  Hie 
square  of  Hie  velocity. 

[6-]  *  = 

136.  Destructive    effects    of    collision.      When    railway 
trains  come  in  collision,  the  engines  are  shattered  by  their 
striking  force,  while  the  momentum  of  the  trains  following 
each  has  been  known  to  pile  thirty  cars  one   above   another. 
The  collision  between  two  ships  of  equal  size  is  the  same 
as  if  either,   at   rest,   had   been   struck  by  the  other  with 
twice  the  velocity.     When  a  large  ship  runs  down  a  small 
vessel,  it  suffers  little  injury,  because  of  its  stronger  build 
and  greater  mass.     Even  light  and  soft  bodies,  as  air  and 
water,  have  tremendous  power  when  moving  rapidly,  as  in 
hurricanes  and  storms. 

CENTER   OF   GRAVITY. 

137.  A  body,  unsupported,  falls  to  the  ground;    and,  if 
supported,    exerts    a    certain    pressure,    called    its    weight. 
These  are  but  special  examples  of  a  force,  of  whose  nature 
nothing  is  certainly  known,  which  acts  upon  all  particles  of 
matter  in  the  universe,  and  constantly  tends  to  make  them 


64 


NA  T  URA  L  PHIL  OS  OP II Y. 


approach  each  other.  Newton  has  shown  that  the  motions 
of  all  the  heavenly  bodies  are  due  to  this  force,  which  he 
called  Universal  Gravitation.  As  applied  to  bodies  on  or 
near  the  earth,  it  is  called  Terrestrial  Gravitation,  or  simply 

Gravity. 

138.  It  will  be  shown  (213)  that  gravity  acts  with  equal 
intensity  upon  the  particles  of  all  bodies,  however  they  may 
differ  in  form,  size,  or  state.  The  direction  and  point  of 
application  of  gravity  will  now  be  considered. 

The  direction  of  gravity.  Weights  dropped  at  differ- 
ent places  on  the  earth's  surface  will  fall  toward  a  point 
at,  or  near,  the  earth's  center.  Hence,  the  direction  of 
the  force  of  gravity  may  be  considered,  without  sensible 
error,  as  the  line  joining  the  point  of  application  and  the 
earth's  center.  This  direction  may  readily  be  found,  at 
any  place,  by  a  plumb  line,  which  consists  of  a  heavy 
weight  suspended  by  a  light  and  flexible  string.  If  a 
plummit  hangs  so  that  the  weight  dips  in  a  vessel  of  water, 
the  line  and  the  surface  of  the  water  will  be  at  right  angles 
to  each  other.  The  direction  of  the  line  at  any  place  is 

called  the  vertical,  and 

IT 

a  line  at  right  angles 
to  it  is  called  a  horizon- 
tal line.  If  two  plumb 
lines  are  placed  near 
each  other,  their  lines 
—  v"  of  direction  will  be  sen- 
sihly  parallel,  because 
their  lengths  are  incon- 

H^^^^^H  siderable  in  comparison 

with  the  radius  of  the 
earth.  Hence,  the  di- 
rection sol'  the  force  of 
gravity  on  particles 
near  each  other  arc  parallel.  In  Fi(ir.  21),  vertical  lines  on 
the  earth  are  designated  by  V,  and  horizontal  line.-  by  H. 


V'"" 


POINT   OF  APPLICATION. 


65 


139.  The  point  of  application  of  gravity.     As  gravity 
acts  in  a  vertical  direction  upon  each   particle  of  a  body, 
its   effect  on  the  body,  taken   as  a  coherent  mass,  will  be 
the   same   as   the   resultant  of  an  infinite  number  of  equal 
and  parallel  forces.     When  the  form  and  dimensions  of  a 
body  are  known,  this  resultant  may  readily  be  calculated 
by  Case  V  (125),  but  in  all  cases  it  may  be  determined  by 
experiment. 

Let  A  B  be  any  body ;  represent  the  force  of 
gravity  on  each  point  by  the  dotted  vertical  lines, 
and  their  resultant,  G  E,  by  the  arrow.  Then,  if 
any  point,  as  C,  in  the  direction  of  this  resultant 
be  supported,  the  body  will  remain  at  rest,  and 
all  the  forces  will  be  expended  in  pressure  on 
the  fixed  point  C.  If,  now,  we  suspend  the  body 
by  a  string  in  the  direction  of  the  line  D  E,  it 
will  still  remain  at  rest,  because  the  line  is  the 
prolongation  of  the  direction  of  the  resultant. 

If,  however,  we  were  to  attach  the  string  to  a 
point  at  P,  outside  of  the  direction  D  E,  the  body 
would  not  remain  at  rest.  The  resultant,  acting 
at  C,  will  be  decomposed  into  two  parts,  the  first  acting  in  the  line 
C  H,  representing  the  wTeight  supported  by  the  point  P,  and  the  second 
acting  in  the  direction  C  I,  which  would  move  the  body  toward  the 
vertical,  P  K.  Therefore,  a  body  supported  by 
a  fixed  point,  can  not  remain  at  rest  unless  the 
direction  of  the  resultant  of  gravity  passes 
through  that  point. 

Now  suspend  the  body  at  another  point,  as  Z, 
the  direction  will  change  its  position ;  but 
whatever  be  the  number  of  directions  thus 
found,  they  will  all  intersect  in  a  common  point, 
as  G. 

140.  The  common  point  of  intersection 
cf  the  resultants  of  the  forces  of  gravity 

in  all  positions  of  the  body  is  called  the  center  of  gravity. 
This  center  may  readily  be  found  in  a  board,  or  a  plate  of 
lead,  by  suspending  it  at  various  points.  A  plumb  line 
attached  to  each  point  of  suspension,  will  show  the  direction 
of  the  resultants. 
N.  P.  5. 


66  NATURAL   PHILOSOPHY. 

The  center  of  gravity  may  be  regarded  as  the  point  of 
application  of  the  force  of  gravity  on  all  the  particles  of 
a  body,  since  it  is  the  only  point  common  to  all  the  result- 
ants. Hence,  in  calculations,  the  weight  of  a  body  may  be 
considered  as  concentrated  in  the  center  of  gravity.  The  ver- 
tical line  passing  through  the  center  of  gravity  is  called  the 
line  of  direction. 

When  the  center  of  gravity  is  supported,  the  body  will 
remain  at  rest,  because  any  resultant  will  be  supported 
when  this  point  is  supported.  Therefore,  the  center  of  gravity 
is  the  point  about  which  all  parts  of  a  body  balance. 

141,  In  bodies  of  uniform  density  the  center  of  gravity 
will  coincide  with  the  center  of  the  figure.  When  such  a 
body  is  symmetrical,  the  determination  of  the  center  of 
gravity  becomes  a  simple  geometrical  problem.  Thus,  the 
center  of  gravity  will  lie  : 

1.  In  a  straight  line,  at  its  center. 

2.  In  a  circle,  at  the  intersection  of  any  two  diameters. 

3.  In  a  parallelogram,  at  the  intersection  of  its  diagonals. 

4.  In   a   triangle,    at  the  intersection  of  the  lines  drawn 
from  the  vertices  of  the  angles  to  the  middle  point  of  the 
side    opposite,  and    at    a    distance    from    any  such   middle 
point  equal  to  one-third  of  the  length  of  the  given  line. 

5.  In  a  sphere,  at  its  center. 

6.  In  a  cylinder,  at  the  center  of  its  axis. 

7.  In  a  parallelopipedon,  at  the  intersection  of  its  diag- 
onals. 

8.  In   a  pyramid,    on   its  axis,   one-fourth  of  its   length 
from  the  base. 


Tin-.-  n-iilN  may  be  verified  by  balancing  bodies,  of  the  figures 
described,  at  the  points  designated.  For  tbe  first  four,  figures  may 
be  made  of  thin  sheets  of  pasteboard,  wood,  or  metal;  for  the  re- 
mainder, the  solids  may  he  made  of  light  wood,  hard  soap,  etc. 

When  the  fi^im-  is  irregular,  the  center  of  gravity  may  be  deter- 
mined by  suspending  it  so  that  it  will  move  freely  from  any  two 


CENTER    OF  GRAVITY. 


67 


{mints,  not  lyintf  in  the  same  line  of  direction,  as  described  in  (139). 
The  intersection  of  the  two  lines  of  direction  will  be  the  center  of 
gravity  sought. 


FIG.  32. 


FIG.  33. 


142,  The  center  of  gravity  may  lie  entirely  outside  of 
the  body,  as  will  be  its  position  in  a  ring,  a  hollow  box,  or 
ball,  or  cask,  yet  even  in  this  case  its  properties  will  be  the 
same  as  if  included  in  the  mass  of  the  body. 

143.  When  two  bodies  are  connected  so  as  to  form  a 
rigid  mass,  the  center  of  gravity  will  be  at  a  distance  from 
either  body,  inversely  as  their  weights.     In  Fig.  34,  if  the 
weights  are  equal,  they  will  be  bal- 
anced  at   the   middle    point   of   the      (~J\ c /^\ 

bar  connecting  them  ;    if  A  is   the  FlG  ^ 

heavier,   the  center  of  gravity  will 

lie  nearer  it.  Thus,  if  A  weighs  four  pounds  and  B 
one  pound,  the  center  of  gravity  will  lie  four  times  nearer 
A  than  B.  When  more  than  two  bodies  are  connected, 
the  center  of  gravity  of  the  compound  body  is  found  by 
taking  them  successively  in  pairs,  in  the  manner  described 
for  finding  the  resultant  of  several  forces.  (124.) 

When  a  body  is  not  of  uniform  density  throughout,  the 
determination  of  the  center  of  gravity  is  similar  to  that  of 
two  bodies  connected. 


68 


NATURAL   PHILOSOPHY. 


144.  Equilibrium  of  heavy  bodies.  Although  a  body  will 
remain  in  a  state  of  rest  when  its  center  of  gravity  is  sup- 
ported, yet,  as  the  center  of  gravity  always  tends  toward  the 
lowest  possible  position,  the  equilibrium  of  a  body  supported 
on  a  fixed  point,  will  depend  on  the  relative  position  of  that 
point  to  the  center  of  gravity.  There  will  thus  be  three 
states  of  equilibrium :  (1.)  stable,  (2.)  unstable,  (3.)  neutral 

1.  A  BODY  IS  IN   STABLE   EQUILIBRIUM    if  it  tends   to    re- 

turn  to  its  original  position  after  it  has  been  somewhat  dis- 
placed. This  will  always  be  the  case  when  any  change  of 
position  elevates  the  center  of  gravity.  A  pendulum  oscil- 
lates about  its  position  of  stable  equilibrium,  and  will 
finally  come  to  rest  in  that  position. 

2.  A  BODY  is  IN  UNSTABLE  EQUILIBRIUM  when  it  tends 
to  depart    farther  from   its   original   position,   after   it  has 
been   slightly   displaced.     This   will  be  the  case  when  the 
point  of  support  is  below  the  center  of  gravity,  for  the  center 
of  gravity  will    then   be   higher  than    in    any  adjacent   posi- 
tion, and  when  removed  from  the 
vertical    above    the   point   of  sup- 
port,   will    not    stop    until    it    has 
gained  the  lowest  possible  position. 
This   is   illustrated    in    balancing  a 
pencil  by  its  point  on    the  tip  of 
the  finger.     Once  balanced,  it  will 
remain   in   equilibrium    until   it   is 
disturbed,    but    the    least   displace- 
ment will   throw  the  line  of  direc- 
tion beyond  the  point  of  support, 
and   the  pencil  will  fall.      If,    now, 
we   attach    a    couple   of   knives  on 
cadi    side    of   the    pencil,    like   the 
balls  in  Kiir.  35,  the  center  of  gravity 
of  the  compound  body  will  he  below 
the  point  of  support,  and  the  body 
will  be  in  .-table  equilibrium. 


ILIBRIUM. 


69 


The  conversion  of  unstable  into  stable  equilibrium,  may  be  illus- 
trated by  suspending  a  pail  from  the  end  of  a  stick  lying  on  the 
edge  of  the  table — Fig.  36.  Now  place  a  second  stick,  E  G,  with  one 


II 


FIG.  36. 

end  against  the  corner  of  the  pail,  and  with  the  other  end  in  a  notch 
cut  in  the  horizontal  stick  C  D.  By  this  contrivance,  the  center  of 
gravity  is  brought  under  the  edge  of  the  table,  and  the  whole  will 
therefore  be  in  stable  eqilibrium.  The  pail  may  now  be  filled  with 
water  without  changing  the  equilibrium. 

3.  A  BODY  is  IN  NEUTRAL  EQUILIBRIUM  when  it  remains 
at  rest  in  any  adjacent  position  after  it  has  been  displaced. 
This  will  be  the  case  when  the  point  of  support  coincides 
with  the  center  of  gravity,  as  when  a  wagon  wheel  is  sus- 
pended on  its  axle.  A  perfect  sphere,  resting  on  a  hori- 
zontal plane,  is  in  neutral  equilibrium,  because  its  center  of 
gravity  is  neither  raised  nor  lowered  in  any  adjacent  posi- 
tion. The  following  figure  represents  three  cones :  A  in 


FIG.  37. 


The 


stable,  B  in  unstable,  and  C  in  neutral  equilibrium, 
position  of  the  center  of  gravity  is  indicated  by  g. 

145.  The  relation  which  the  center  of  gravity  bears  to  equi- 
librium, may  be  shown  by  the  following  simple  contrivance. 


70  NATURAL  PHILOSOPHY. 

Thrust  two  half  knitting 
needles  and  one  whole  one 
through  a  cork,  at  right 
angles  to  each  other,  and 
support  the  apparatus  on  two 
wine  glasses,  by  one  of  the 
shorter  needles.  By  pushing 
the  vertical  needle  up  or 
down,  the  center  of  gravity 
FIG.  38.  can  be  altered  at  pleasure, 

and    the   apparatus    brought 

into  either  stable  or  unstable  equilibrium.  In  performing  this  ex- 
periment, the  student  should  carefully  notice  the  position  of  the 
center  of  gravity,  when  the  apparatus  best  exhibits  the  slate  of  stable 
equilibrium,  for  this  is  the  position  required  in  a  good  balance. 

146.  This  experiment  shows  that  the   preceding  distinc- 
tions apply  to  bodies  resting  on  two  or  more  fixed  points. 
The  pressure   on   these  points  is  manifestly  equal    to  the 
resultant   in   the   line   of  direction.      Thus,    a   book  is   in 
stable  equilibrium  when  resting  on  its  side,  and  in  unstable 
equilibrium  when  standing  on  its  edge. 

When  a  body,  supported  on  two  points,  is  in  equilibrium,  the 
line  of  direction  will  pass  through  the  line  connecting  the  points 
of  support.  Thus,  a  man  standing  on  stilts  is  in  a  state  of  unstable 
equilibrium.  So,  also,  is  a  man  walking  on  a  tight  rope.  The  latin- 
uses  a  long  pole,  which  he  elevates  or  depresses,  t<>  a-ist  him  in 
keeping  the  center  of  gravity  vertically  over  the  rope.  A  person 
walking  on  the  thin  edge  of  a  plank  throws  out  his  arms  for  the 
same  reason. 

147.  The  stability  of  bodies.     When  a  body  has  but  one 
point  of  support,  or  rests   upon   ;i   line,  it  is  easily  moved 
from   the  vertical,  and  can   not  be  said  to  possess  stobUihj. 
This  property  depends  on   the  relation  which   the  center  of 
gravity  bears  to  at  lea>t  three  point-,  not  in  the  same  straight 
line,  which  constitute,  the  base  of  the  body.     The  base  of  a 
body  supported    on   le^s,  as  a  table,   i>   the  polygon  formed 
by  lines  connecting  the  bottom  of  the  legs. 

A  b«»dy  re-tin^  on  a  hsisc  is  .-table,  when  the  line  of 
direction  fulls  within  the  ban-.  The  stability  of  such  bodies 


EQUILIBRIUM. 


71 


may  be  estimated  by  the  force  required  to  overturn  them. 
If  its  position  can  be  changed  without  raising  the  center  of 
gravity,  the  slightest  force  would  be  competent  to  move  it, 
if  friction  did  not  oppose.  If  its  position  can  not  be 
changed  without  raising  the  center  of  gravity,  then  the 
force  required  to  move  it  must  be  sufficient  to  raise  the 
entire  body  to  the  same  height  that  the  center  of  gravity 


would  be  elevated.  To  illustrate  this,  let  the  diagrams,  Fig. 
39,  represent  sections  drawn  through  the  center  of  gravity 
of  different  solids,  and  denote  their  centers  of  gravity  by  G. 
To  turn  either  of  these  bodies  over  the  edge  E,  the  center 
of  gravity  must  pass  through  the  arc  G  T,  and  be  raised 
through  the  height  H  T.  A  careful  inspection  of  these 
figures  will  lead  to  the  following  deductions: 

The  distance,  H  T,  increases  as  the  ratio  of  the  height 
to  the  base  decreases:  therefore,  (1.)  the  stability  of  bodies 
of  the  same  height  and  similar  figure  is  increased  by  widen- 
ing the  base. 

The  distance,  H  T,  increases  in  proportion  as  the  center 
of  gravity  is  lowered:  therefore,  (2.)  the  stability  of  bodies 
is  increased  by  bringing  the  center  of  gravity  to  the  lowest 
possible  position. 

As  a  corollary  to  this;  (3.)  of  bodies  having  the  same 
height  and  base,  but  of  dissimilar  figures,  the  pyramid  is  the 
most  stable. 

Now,  if  the  similar  sections,  in  Fig.  40,  inclined  more  or 
less  from  the  perpendicular,  be  compared,  it  will  be  seen, 
(4.)  that  the  stability  of  bodies  is  greatest  when  the  line 
of  direction  passes  through  the  center  of  the  base. 

So  long  as  the  line  of  direction,  G  D,  falls  within  the 


72 


NATURAL   PHILOSOPHY. 


base,  the  body  will  stand,  but  its  stability  will  be  less  in 
proportion  as  its  distance  from  the  center  of  the  base  in- 
creases, until  the  line  of  direction  falls  exactly  through  the 
edge,  E.  In  this  position  the  body  is  in  a  state  of  unstable 


equilibrium,  and  will  be  overturned  by  the  slightest  force. 
Finally,  (5.)  when  the  line  of  direction  falls  without  the 
base,  the  center  of  gravity  will  be  unsupported,  and  the 
body  will  fall. 

148.  A  sphere  remains  at  rest  on  a  horizontal  plane,  be- 
cause the  line  of  direction  passes  through  the  point  of  sup- 
port, but  if  the  plane  be  inclined, 
the  line  of  direction  will  fall  with- 
out  the  base,   and   the   sphere  will 
roll"  downward.     So,    any  body   on 
an    inclined    plane,    will    not    slide 
down   the  plane,    until   the  line  of 
direction  has  fallen  so  far  forward  as 
to  overcome  the  friction  of  the  plane. 

149.  Practical  applications.     (1.)  Stability  dependent  on 
extent  of  base:    candlesticks   and   inkstands  are   made  with 
broad  bases.     Stone  walls  are  broader  at  the  Imse  than  at 
the    top.      Tall    monuments    are    made    with    their    sides    in- 
clined, and  often  have  very  Isirirr  bases.      The  le^s  of  chairs 
are  inclined  outward.      A  child's  hijrh  chair  has  a  very  wide 

_.  i  Stability  dependent  on  the  height  of  the  center 
of  gravity:  a  load  of  hay  is  more  easily  overturned  than 
the  same  woiirht  of  stone.  In  loading  a  wa.iron  or  a  ship, 
the  heavier  articles  should  l»e  placed  at  the  bottom.  (3.) 
Stability  dejM-ndent,  on  the  line  of  direction.  There  are 


Fio.  41. 


RECAP/TULA  TION. 


73 


many  towers  in  Italy,  as  at  Pisa  and  Bologna,  which  incline 
far  from  a  perpendicular  position,  but  in  these  the  line  of 
direction  still  falls  within  the  base. 

150.  General  considerations.  The  center  of  gravity  in  man 
lies  between  his  hips,  his  base  is  the  area  inclosed  by  his  feet.  The 
different  attitudes  assumed  by  persons  in  standing  or  moving  are  the 
ivsults  of  instinctive  efforts  to  keep  the  line  of  direction  within  the 
points  of  support.  In  standing,  a  man  widens  his  base  by  turning 
out  his  toes,  or  by  using  a  cane.  In  moving  about,  the  center  of 
gravity  is  perpetually  changing,  and  the  positions  of  the  several 
parts  of  the  body  are  changed  to  correspond.  Thus,  when  a  person 
rises  from  a  chair,  he  either  throws  his  body  forward,  or  draws 
his  feet  backward,  to  bring  the  center  of  gravity  over  his  feet.  In 
running  or  ascending  a  hill,  a  person  throws  his  body  forward  so  as 
to  carry  his  weight  with  less  effort.  In  descending  a  hill,  he  leans 
backward,  so  that  his  weight  shall  not  cause  him  to  fall  forward.  A 
man  standing  with  his  heels  against  a  vertical  wall,  finds  it  difficult 
to  stoop  to  the  floor  without  falling. 

When  a  person  carries  a  load,  the  effort  is  to  preserve  the  line  of 
direction,  common  to  himself  and  the  load,  within  his  base.  If  the 
load  is  in  his  right  hand,  the  person  inclines  his  body  to  the  left,  and 
throws  out  his  left  hand  as  an  additional  assistance.  If  the  person 
carries  the  load  on  his  head,  or  an  equal  portion  in  each  hand,  there 
is  no  tendency  to  lean  to  either  side.  If  the  load  is  on  his  back,  he 
bends  forward ;  if  carried  in  his  arms,  he  leans  backward. 

151.  Recapitulation. 
I. 


Mechanics  considers 


r  Equilibrium  of 


Motion  of 


r  Solids Statics, 

-I  Liquids.. Hydrostatics, 

v  Gases Aerostatics. 

f  Solids. ...Dynamics, 

•j  Liquids..Hydrodynamics, 


..Aerodynamics. 


II. 


Motion  is  classified 


With  regard  to  a  given  (  Absolute, 
point.  \  Relative. 

(  Uniform, 
Witli  regard  to  rate,    j  yar;e(j 

f  Simple, 
L  With  regard  to  force. 


74  NATURAL   PHILOSOPHY. 

III. 

{1.  The  inertia  of  bodies. 
2.  The  action  of  forces. 
3.  Action  and  reaction. 

IV. 

f  Stable — support  above  center. 

Equilibrium  is \  Unstable — support  below  center. 

I  Neutral — support  at  center. 

STATICS. 

152.  Hitherto  we  have  considered  the  action  of  forces  as 
directly  applied  to  bodies;  but  there  are  many  instances  in 
which   force   acts   indirectly,    through   the   intervention   of 
some  instrument. 

Thus,  it  is  possible  to  arrange  the  burning  coals  in  a  grate  by  the 
direct  application  of  the  hands,  but  it  is  certainly  safer  and  more 
convenient  to  apply  the  requisite  force  to  a  poker,  which  will  com- 
municate it  to  the  coals.  The  poker  then  becomes  a  machine. 

153.  A  machine  is  an  instrument  by  means  of  which  a 
force,  applied  at  a  certain  point,  is  made  to  exert  force  at 
another   point,    more   or   less   distant.     The  effective   force 
generally  differs  in  intensity  from  the  force  applied. 

The  force  employed  in  a  machine  is  called  the  power. 
The  resistance  overcome  by  a  machine,  at  the  point  where 
the  power  acts,  is  called  the  weight  or  load.  It  may  be  con- 
sidered as  a  force  acting  in  a  direction  opposite  to  that  of 
the  power.  The  work  is  the  product  of  either  the  power  or 
the  load,  by  the  vertical  space  through  which  it  moves. 

154.  The  foot-pound.     In  order  to  estimate  the  efficiency 
of  any  force,  an  arbitrary  unit  of  work  has  been  adopted, 
called   the  foot-pound.     The   foot-pound   is   the   mechanical 
value  of  a  force  capable  of  raising  one  pound    through   a 
vertical    space  of  one  foot.      The  work   of  the  power  is, 
therefore,  equal   to  the  product   of  an   equivalent    weight  in 
pounds   multiplied   by  the  vertical  height  in   feet   through 


HORSE-POWER.  75 

which  it  passes.     The  work  of  the  load  is  found  in  a  similar 
manner. 

Thus,  to  raise  a  load  of  one  thousand  pounds  of  water  thirty- 
three  feet  high,  requires  a  power  equal  to  thirty-three  thousand  foot- 
pounds. 

155.  Horse-power.     To  estimate  the  work  of  any  force, 
acting  through  a  limited  period  of  time,  another  unit  has 
been  adopted,  called  the  horse-power.     A  horse-power  is  the 
mechanical  value  of  a  force  capable  of  raising  thirty-three 
thousand  pounds   one   foot   in   one   minute.      Its  work  is, 
therefore,  equal   to   thirty-three  thousand   foot-pounds  in  a 
minute. 

Thus,  one  horse-power  can  raise  one  thousand  pounds  thirty-three 
feet  high  in  one  minute,  or  five  hundred  and  fifty  pounds  one  foot 
high  in  a  second,  or  one  million  nine  hundred  and  eighty  thousand 
foot-pounds  in  an  hour. 

156.  No   machine   can   create  power.     It  is   merely  an 
inert  instrument  for  the  advantageous  application  of  power. 
In  explaining  the  theory  of  machinery,  many  circumstances 
are  at  first  neglected  which  must  afterward  be  taken  into 
account.     Thus,  it  is  assumed  that  the  parts  of  a  machine 
move  without  friction,  without  resistance  from  the  air,  that 
they  have  neither  weight  nor  inertia;    also,  that  the  ropes 
and  chains  employed   have  neither  thickness,  stiffness,  nor 
weight.     As  these  conditions  are  never  satisfied,  a  part  of 
the  power  must  be   expended   in   the   machine  itself,  and 
hence  power  is  partially  lost  when  applied  to  machines. 

157.  The  work  of  the  power  is  always  equal  to  the  work 
of  the  load.     Hence,  if  any  machine  will  enable  us  to  lift 
a  weight  of  ten  pounds  by  a  power  of  one  pound,  (1.)  the 
power  must  move  ten  times  the  space  traversed  by  the  load ; 
(2.)    as   the   spaces   are   traversed   in    the   same   time,    the 
power  must  move  ten  times  as  fast  as  the  load.     Therefore, 
the    following    laws   are   applicable   to    machines   of  every 
kind: 


76  NATURAL   PHILOSOPHY. 

1.  The  power  -multiplied  by  Hie  vertical  <li.<t<tnce  through  ivhich 
it  passes  equals  the  load  multiplied  by  Hie  vertical  distance  through 
whiefi  it  passes. 

[7.]     PD  =  LD'. 

2.  Tlie  power  multiplied  by  its  velocity  equals  the  load  multi- 
plied by  its  velocity. 

[8.]     PV  =  LV. 

158,  If  we  reverse  the  conditions  given  in  the  previous 
example,  and  suppose  a  power  of  ten  pounds  to  be  required 
to   move  a  weight  of  one  pound,  the  laws  will  still  hold 
good;  but  the  results  will  be  exactly  opposite,  that  is,  the 
load  will   traverse  ten   times  the  space,  with  ten  times  the 
velocity  of  the    power.     We  see,  therefore,   that    machines 
will  enable  us  (1.)  to  economize  our  force  by  making  it  act 
with  great  velocity,  to  move  heavy  loads  very  slowly;    or 
(2.)    to   economize   our  time,  by  the   expenditure  of  great 
power  to   move   small    loads    very    rapidly.     Practical    me- 
chanics express  this   fact  by  the   axiom,  "  What  is  gained 
in  power  is  lost  in  velocity." 

159.  Among  the  many  advantages  derived  from  the  use 
of  machinery  are: 

1.  It  enables  us  to  employ  our  whole  force  at  the  same 
time. 

A  person  winding  thread  on  a  reel  will  expend  only  a  small  part 
of  his  strength ;  suitable  machinery  will  enablr  him  to  turn  many 
reds  at  once. 

2.  It  enables  us  to  change  the  direction  of  our  force. 

A  sailor  may  hoist  the  sails  of  his  ship  while  Mainline  on  the  deck, 
in-ifiid  of  elimbiiiL:  the  m;i.-t  ami  laboriously  pulling  them  up. 

3.  It  enables   us  to  perform    work   \ve  could   not   do  with 
our  una  —  i-t<  d  >trength. 

By  using  a  crow-bar,  a  man  may  rai-r  a  large  stone,  which  he  could 
not  stir  with  his  liaml-. 


TIIK   LEVER.  77 

4.  It  enables  us  to  employ  other  forces  than  our  own,  as 
the  strength  of  animals,  the  forces  of  wind,  water,  and  steam. 

5.  It  enables  us  to  utilize  the  products  of  nature. 

It  is  the  knowledge  of  machinery  that  distinguishes  civilized 
nations  from  savages,  since  by  it  we  have  mills  for  weaving  cloth, 
forging  iron,  grinding  flour,  etc. 

160.  All  machinery  may  be  reduced  to  six  elementary 
forms,   called  simple  machines.      The  simple   machines  are 
(1.)   the   lever,  (2.)   the  wheel   and  axle,  (3.)   the  pulley, 
(4.)  the  inclined  plane,  (5.)  the  wedge,  (6.)  the  screw.     A 
combination  of  two  or  more  of  these  constitutes  a  compound 
machine. 

161.  A  lever  is  an  inflexible  bar  moving  freely  about  a 
fixed  point,  called  a  fulcrum. 

The  arms  of  the  lever  are  the  parts  into  which  the 
fulcrum  divides  it.  When  the  arms  are  not  in  the  same 
straight  line,  it  is  called  a  bent  lever;  otherwise,  simply  a 
lever. 

There  are  three  classes  of  levers,  depending  on  the  rela- 
tion of  the  power,  load,  and  fulcrum. 

In  levers  of  the  first  kind, 
the  fulcrum  is  between  the 
power  and  the  load,  as  in 
Fig.  42,  I.  In  levers  of  the 
second  kind,  the  load  is  be- 
tween the  power  and  the  ful- 
crum, as  in  Fig.  42,  II.  In 
levers  of  the  third  kind,  the 
power  is  between  the  load  and 
the  fulcrum,  as  in  Fig.  42, 
III.  The  lever  acts  on  the 
principle  of  parallel  forces. 
The  power  and  the  load  will 

FIG.  42. 

be  in  equilibrium  when  they 

are  inversely  as  their  distance  from  the  fulcrum. 


78  NATURAL   PHILOSOPHY. 


[9.]     P  :  L  :  :   W  F  :  P  F  ;  or,  P  X  P  F  =  L  X  W  F. 

[10.]     P  =  ^S  [11.]    L=PX1? 

P  F.  W  F. 

162.  STATICAL  LAW.  —  The  product  of  the  power  multiplied 
by  its  distance  from  the  fulcrum,  is  equal  to  the  product  of  the 
load  multiplied  by  its  distance  from  the  fulcrum. 

A  statical  law  expresses  the  relation  of  the  power  and 
load  when  a  machine  is  in  exact  equilibrium.  To  produce 
motion  it  is  necessary  that  one  product  should  exceed  the 
other.  The  greater  product  will  determine  the  direction 
of  the  motion. 

EXAMPLES.  —  In  a  lever  of  the  first  kind,  sixteen  inches  long,  with 
the  fulcrum  four  inches  from  the  load,  a  power  of  one  pound  will 
balance  a  load  of  three  pounds. 

In  a  lever  of  the  second  kind,  sixteen  inches  long,  with  the  load 
four  inches  from  the  fulcrum,  a  power  of  one  pound  will  balance  a 
load  of  four  pounds. 

On  a  lever  of  the  third  kind,  sixteen  inches  long,  with  the  power 
four  inches  from  the  fulcrum,  a  po\ver  of  one  pound  will  balance  a 
of  one-fourth  of  a  pound. 


163.  Familiar  illustrations.  A  poker  is  a  lever  of  the 
first  kind,  when  it  raises  the  coals  in  the  grate  by  resting 
on  the  bars  of  the  grate  as  a  fulcrum.  A  crow-bar  is  used 


KM;.  43.  Fid.  44. 

as  a  lever  of  the  first  kind  when  we  pn-ss  downward  to 
rai~r  the  loud  above  a  block  used  as  a  fulcrum.  Fig.  43. 
It  is  also  used  as  a  lever  of  the  second  kind,  when  one  end 
rests  on  the  Around  as  a  fulcrum,  and  \\c  lift  upward  to 
raise  the  load.  Fi<r.  44.  A  fishing-rod  is  a  lc\cr  of  the 
third  kind;  tin-  fish  h<-m_Lr  the  load,  and  the  power  is  ap- 
plied between  it  and  the  other  end  of  the  rod.  The  hinges 


BENT  LEVERS. 


79 


of  a  door  are  its  fulcra,  the  load  is  at  the  center  of  gravity 
of  the  door ;  in  closing  it,  if  the  hand  be  applied  near  the 
latch,  the  door  is  a  lever  of  the  second  kind,  but  if  the 
hand  be  near  the  hinges,  the  door  is  a  lever  of  the  third 
kind.  Scissors,  snuffers,  and  pincers  are  double  levers  of 
the  first  kind,  the  pivot  being  the  fulcrum,  and  the  load  the 
object  between  the  blades.  Nut-crackers  are  double  levers 
of  the  second  kind.  Tongs  are  double  levers  of  the  third 
kind. 

164.  In   levers   of  the   first   kind,   the   power  may  be 
greater,  equal  to,  or  less  than  the  load,  according  to  the 
relative   distance   from   the   fulcrum.     Thus,  in   cutting   a 
strip  of  cloth  with  a  pair  of  scissors,  the  power  exceeds  the 
load,  until  we  have  cut  a  distance  from  the  pivot  equal  to 
that  of  the  hands ;  at  this  point  the  power  equals  the  load, 
but  beyond   that  the  load  will    require  a   greater  power. 
As   they  are  generally  used,    intensity  of  force  is  gained 
with  levers  of  the  first  and  second  kinds.     They  are,  there- 
fore, employed  to  move  heavy  weights  with  small  powers. 
Their  efficiency  may  be  increased,  (1.)   by  increasing  the 
power,  (2.)  by  increasing  its  relative  distance  from  the  ful- 
crum. 

In  levers  of  the  third  kind,  intensity  of  force  is  always 
lost;  wre,  therefore,  employ  this  lever  when,  we  wish  to 
move  small  weights  rapidly  by  the  use  of  greater  powers. 

165,  Bent   levers.      When    the 
arms  of  the  lever  are  bent,  or  wrhen 
the  power  and  weight  do  not  act 
parallel   to    each   other,    their    re- 
spective distances  are  reckoned  by 
perpendiculars    drawn    from    the 
fulcrum    to   the   direction    of   the 
power  and  the  load.     This  is  ex- 
emplified  by  the   bent   lever  bal- 
ance shown  in  Fig.   45.       In    this 
the   power  is   constant.      As   the 


w 


FIG.  45. 


80 


NATURAL  PHILOSOPHY. 


load  is  increased,  it  depresses  the  scale  bar.  By  this  means, 
the  leverage  of  the  shorter  arm  is  diminished*  while  that 
of  the  longer  arm  is  increased.  The  claw  of  a  hammer 
used  in  drawing  out  nails,  is  another  example;  the  load  is 
the  friction  of  the  nail,  the  hand  applies  the  power,  and  the 
edge  of  the  hammer  is  the  fulcrum. 

166.  When  a  beam  rests  on  two  props  and  supports  a 
weight  between  them,  the  amount  supported  by  either  prop 
may  be  estimated   by  considering  it  as  the  power,  and  the 
other  prop  as  the  fulcrum.     The  lever  will  be  of  the  second 
kind.     If  A  and  B  carry  a  load  between  them  on  a  pole, 

each  man  will  bear 
half  the  burden,  if  the 
weight  hangs  from  the 
middle  of  the  pole. 
If,  however,  the  weight 
is  one-third  of  the 
length  of  the  pole  from 
A,  he  will  bear  two- 
thirds  of  the  burden 
and  B  one-third.  The 
load  sustained  by  each 
is  inversely  as  the  dis- 
tance between  them 
and  the  load.  Two 
horses  attached  to  a  wagon  may  be  made  to  pull  unequal 
loads  by  placing  the  bolt  of  the  whippletree  nearer  the 
stronger  horse. 

167.  When  a  small  force  is  required  to  sustain  a  consid- 
erable weight,  and  it  is  not  convenient    to  use  a   loni:  lever, 
a  combination    of  levers,   called    a    foini>oiuid  lever,  may  be 
employed.      When  a  compound   l<-vcr  is   in   equilibrium,  the 
power  iHH/fiji/inl   hif  tin'   fonfiinird   fii-mlud    <>t'   t/n    dlterncite 

arm*,   i-nmnn  in-i,i<j  irith   tlir  jmiri  i\   rifim/*  llir   /iniil   in  it/t ifi/i'd  hij 

the  continued  product  of  the  alternate  arm*,  commencing  with 
the  load. 


FIG.  46. 


COMPOUND   LEVER. 


81 


In  the  arrangement  shown  in  Fig.  47,  AF  and  A"  F"  are  levers 
of  the  second  kind,  and  A'  B'  a  lever  of  the  first  kind.  The  power 
P,  acting  on  the  lever  A  F,  produces  a  downward  force,  at  B,  as 
many  times  greater  than  itself  as 
the  distance  A  F  is  greater  than 
B  F.  If  A  F  is  ten  times  greater 
than  BF,  the  force  at  B  is  ten 
times  the  power.  This  force  is 
then  transmitted  to  A'.  If  we 
suppose  the  arms  of  the  upper 
lever,  A'  F7  and  F'  B',  to  bear  the 
same  proportion  of  ten  to  one,  the 
force  exerted  at  B'  will  be  ten 
times  that  at  A'  or  B.  Then  the 
force  transmitted  to  A/x  will  be 
one  hundred  times  the  power.  If 
the  arms  of  the  lowest  lever, 
A"  F"  and  B"  F",  are  as  ten  to 

one,  another  increase  of  ten  times  FlG  47 

the  power  will  be  gained ;  hence,  a 

power  of  one  pound  at  P  will  balance  a  load  of  one  thousand  pounds 
at  L. 

168.  When  several  forces  act  upon  the  same  arm  of  the 
lever,  the  effect  of  each  force  must  be  computed,  and  their 
sum  will  be  the  resultant  of  all.     Theoretically,  the  weight 
of  the   lever  does   not  enter  into   the   calculation,  but   in 
experiments  it  is  necessary  to  consider  the  weight  of  each 
arm   as    applied   at   its   center   of  gravity.     We    shall   not 
obtain  satisfactory  results  in  experiments  with  levers  unless 
we  first  balance  the  levers  by  a  sufficient  counterpoise  before  at- 
taching the  power  and  the  load. 

169.  The  practical  applications   of  the  lever  are  very 
numerous.      The    most  common  relate  to  weighing.      Any 
form  of  levers  of  the  first  kind  may  be  used  for  this  pur- 
pose, and  the  student  may  construct  quite  accurate  scales 
for  himself  from  strips  of  stout  wood. 

Tlie  steelyard  is  a  lever  of  the  first  kind,  having  two 
unequal  arms,  and  employing  a  constant  counterpoise. 
Fig.  48.  The  counterpoise  M  is  movable  along  the  beam, 

N.  P.  6. 


82  NATURAL  PHILOSOPHY. 

the  load  is  suspended  from  W  by  a  hook  or  scale  pan,  and 
F  is  the  fulcrum  for  light  loads.  The  beam  is  graduated 
by  bringing  the  counterpoise  into  equilibrium  with  known 
weights  of  different  magnitude,  and  the  position  of  the 


FlQ.  48. 

counterpoise  is  marked  by  a  notch,  and  numbered  for  each 
weight.  A  second  fulcrum  F'  is  used  for  heavier  weights, 
to  avoid  increasing  the  length  of  the  beam.  When  the  bar 
is  turned  half  over,  the  hook  turns  about  the  end  and  falls 
below  the  shorter  arm. 

If  the  center  of  gravity  of  the  unloaded  beam  were  at  the  ful- 
rrum,  the  notches  on  the  beam  would  be  at  a  distance  from  each 
other,  equal  to  that  of  the  hook  and  the  fulcrum,  but,  ordinarily,  the 
longer  arm  predominates.  Hence,  the  zero  point  is  not  at  F,  but  at 
some  point  between  F  and  M. 

170.  The  balance  is  a  lever  of  the  first  kind,  having  two 
equal  arms.  Fig.  49.  Delicate  balances  are  furnished 
with  a  needle  attached  to  the  center  of  motion,  which  oscil- 
lates before  an  index,  n,  to  show  small  deviations  of  the 
beam.  A  balance  is  sensitive,  when  a  very  small  difference 
between  the  weights  in  the  scales  causes  a  perceptible  motion 
in  the  pointer. 

The  center  of  gravity  of  the  balanee  should  be  a  little, 
h»-luw  the  «.<lge  of  the  fulcrum.  This  will  bring  it  to  a 
state  of  stable  equilibrium,  in  which  it  will  m-M  readily 
tend  to  return  to  a  hori/ontal  position.  If  too  far  below, 
it  will  be  less  sensitive,  because  too  stable.  If  the  centers 


THE  BALANCE.  83 

of  gravity  and  motion  coincide,  it  will  be  in  neutral  equi- 
librium. If  the  center  of  gravity  is  above  the  center  of 
motion,  it  will  be  in  unstable  equilibrium,  and  the  heavier 
arm  will  remain  depressed.  Compare  (145). 


FIG.  49. 

The  arms  should  be  precisely  equal  in  length,  otherwise 
one  will  have  a  greater  leverage  than  the  other,  and  unequal 
weights  will  be  required  to  produce  equilibrium.  To  test 
this,  place  weights  in  each  scale  pan,  and  bring  the  beam  to 
a  horizontal  position.  Now  transfer  the  weights  to  the 
opposite  scale  pans.  If  the  beam  remains  horizontal,  the 
arms  are  equal. 

171.  Dishonest  dealers  are  said  to  use  balances  with 
unequal  arms,  placing  their  merchandise,  when  buying,  in 
the  shorter  arm,  but  when  selling,  in  the  longer.  We  can 
not  find  the  true  weight  of  a  body  in  a  false  balance  by 
weighing  it  in  each  scale,  and  then  taking  half  the  sum  of 
the  two  weights,  or  their  arithmetical  mean;  because  the 
body  is  overestimated  by  one  weighing,  in  the  same  ratio 
that  it  is  underestimated  in  the  other.  We  must,  therefore, 
take  the  geometrical  mean  of  the  false  weights,  which  is 
the  square  root  of  their  product.  Thus,  if  a  body  weighs 


84  NATURAL   PHILOSOPHY. 

nine  pounds  in  one  scale  and  four  pounds  in  the  other,  the 
true  weight  is  six  pounds. 

172.  As  all  balances  are  liable  to  become  false,  by  the  unequal 
expansion  of  their  arms,  the  best  method  of  weighing  is  that  known 
as  Borda's  double  weighing,  which  always  secures  accurate  results  in 
a  sensitive  balance.     Place  the  body  to  be  weighed  in  one  scale  pan 
and  counterbalance  it  with  shot,  then  remove  the  body,  and  in  its 
stead  place  known  weights  which  will  exactly  restore  the  equilibrium 
of  the  balance.     These  weights  will  be  the  exact  weight  of  the  body. 

173.  The  compound  lever,  shown  in  Fig.  47,  may  readily 
be  converted   into  a  weighing  machine.      It  only  needs   a 
scale   pan   attached   to  the   chains,    and  a  counterpoise   to 
move    along    the    middle    lever.      The    common    platform 
scales   consist  of  a   system    of  compound  levers,    and   are 
used  for  weighing  heavy  articles. 

174.  The  wheel  and  axle.      The  space  through  which  a 
load  may  be  raised  by  a  single  action  of  the  lever,  is  ordi- 
narily very  small.     To  raise  a  load  higher  than  the  sweep 
of   the  short  arm,  requires  a  repeated   adjustment  of  the 
fulcrum,  and  a  contrivance  for  supporting  the  load  while 
this  is  being  effected.     In  such  cases,  the  action  of  the  lever 
is  intermittent.     When   continuous    motion    is   required,  as 
to  raise  a  box  to  the  top  of  a  building,  the  wheel  and  axle 
is  frequently  employed. 

175.  The  wheel  and  axle  consists  of  a  wheel  and  cylinder, 

firmly  united,  and  free  to  revolve  on  a  com- 
mon axis.  The  power  is  applied  at  the  cir- 
cumference of  the  wheel,  and  tends  to  move 
a  load  applied  at  the  circumference  of  the 
cylinder  or  axle.  This  machine  acts  as  a 
perpetual  lever  of  the  first  kind,  the  ful- 
crum Ix-inir  at  F,  the  common  center,  and 
the  arms  of  the  lever  being  respectively 
AF  and  F  B,  the  radii  of  the  wheel  and 
the  axle.  The  power  and  load  will  he  in 

equilibrium    when    they   are    inversely    proportional    to    the 

radii  <>f  the   wheel  and  the  axle. 


WHEEL  AND  AXLE. 


85 


[12.]     P  :  L  ::  BF  :  AF;  or,  PX  A  F  =  L  X  B  F. 


[13.]   P  = 

L      J  AF. 


[14.]     L  = 


PX  AF 
BF. 


STATICAL  LAW. — The  power  multiplied  by  the  radius  of 
the  wheel  equals  the  load  multiplied  by  the  radius  of  the  axle. 

EXAMPLE. — When  the  wheel  is  six  feet  in  radius  and  the  axle  six 
inches,  a  power  of  one  pound  will  sustain  a  load  of  twelve  pounds. 

176.  In  the  various   forms   of  this    machine,  the   load  is 
generally  attached  to   a  rope  coiled  around   the  axle;    the 
power  is  applied  in  various  ways. 

The  form  represented  in  Fig.  50  is  that  used  in  warehouses,  in 
which  the  power  is  applied  by  means  of  a  rope  coiled  on  the  wheel. 
When  the  rope  on  the  wheel  is  unwound,  that  on  the  axle  is  wound 
up,  and  the  load  raised.  As  radii  are  proportional  to  their  circum- 
ferences, it  is  manifest  that  the  rope  unwound  from  the  wheel  will  be 
as  many  times  longer  than  that  wound  up  on  the  axle,  as  the  load 
exceeds  the  power.  The  power  may  also  be  applied  to  pins  project- 
ing from  the  wheel,  as  in  the  steering  apparatus  on  large  vessels. 

177.  It  is  not  nec- 
essary that  the  power 
be  applied  to  a  com- 
plete   wheel,    since    a 
single  spoke  will  an- 
swer.    This   modifica- 
tion   is    the    windlass 
employed    in    raising 
water  from  wells.    The 
winch    constitutes    the 
power  arm — the  radius 

of  the  axle  the  load  arm.  In  the  windlass  used  on  ships  there  is 
no  fixed  handle,  or  winch,  but  handspikes 
are  fitted  into  slots  cut  in  the  axle,  and 
are  shifted  as  occasion  requires.  When 
the  windlass  has  a  vertical  axis,  it  con- 
stitutes a  capstan.  Fig.  52.  This  is 
turned  by  men  walking  around  it,  and 
pressing  against  handspikes  inserted  in 
52.  the  top  or  drum. 


86 


NATURAL   PHILOSOPHY. 


FIG.  63. 


178.  The  effective   power  of  this  machine  may  be  aug- 
mented by  increasing  the  radius  of  the  wheel,  or  by  dimin- 
ishing that  of  the  axle;   but  very  large  wheels  are  too  un- 
wieldy, and  very 
small   axles    too 
weak  for  practi- 
cal   use.     These 
inconveniences 
may  be  obviated 
by    making    the 
axle  of  two  parts, 
with  different  ra- 
dii,   having    the 
same  rope  so  at- 
tached that,  as  it 
winds       around 
the    thicker,    it 

unwinds  from  the  thinner.     This  contrivance  is  called  the 
differential  wheel  and  axle. 

The  effect  is  to  shorten  the  rope  by  which  the  load  is  suspended,  by 
the  difference  between  the  circumference  of  the  two  parts,  but  the 
height  through  which  the  weight  is  raised  is  only  half  this  shorten- 
ing of  the  rope.  Hence,  the  efficiency  of  the  differential  wheel  and 
axle  may  be  found  by  this  rule :  The  power  multiplied  by  the  radius  of 
the  wheel,  equals  the  load  multiplied  by  half  the  difference  of  the  radii  of 
the  two  parts  of  the  axle. 

By  making  the  two  parts  of  the  axle  of  nearly  the  same  size,  the 
effective  power  m:iy  l>u  increased  to  any  required  amount. 

179.  The  power  of  this  machine  may  also  be  augmented, 
on    the    principle   of   the   compound    lever,    by   combining 
several,  in  such  a  way  that  the  axle  of  the  first  may  act  on 
the  wheel  of  the  second,  and  so   on.     Several  wheels  and 
axles  combined  in  one  machine  are  called  a  train. 

A  train  of  wheels  is  frequently  connected  by  cogs,  as  in 
clock-work.  The  cogs  on  the  wheel-  an-  called  teeth,  those 
on  the  axles,  leaves.  The  axle  itself  is  termed  a  shaft,  or 
pinion.  The  mechanical  power  of  a  train  of  wheels  may  be 


WHEEL   AND  AXLE. 


87 


found  in  the  same  way  as  for  a  compound  lever.  Since 
the  cogs  are  proportionate  to  the  radii  of  the  wheels  and 
pinions,  the  statical  law  may  be  thus  stated:  The  power 


FIG.  54. 


multiplied  by  the  continued  product  of  the  teeth  in  each 
wheel,  equals  the  load  multiplied  by  the  continued  product 
of  the  leaves  in  each  pinion. 


FIG.  55. 


In  Fig.  54,  the  power  is  represented  as  acting  on  the  wheel  which 
carries  the  first  pinion  P.  By  this  arrangement,  a  small  power  is 
capable  of  raising  a  large  load,  but  with  a  corresponding  loss  of 
velocity.  The  arrangement  may  be  reversed  for  the  sake  of  augment- 


88 


NATURAL   PHILOSOPHY. 


ing  the  velocity,  at  the  expense  of  the  power.  Thus,  in  a  watch, 
power  is  applied  to  a  wheel  that  revolves  once  in  four  hours,  to  give 
the  second  hand  a  revolution  once  in  a  minute. 

180.  Toothed  wheels   are   of  three   kinds,    spur,    crown, 
and  bevel. 

Spur  wheels  have  their  teeth  in   the   direction  of  their 
radii,  as  in  Fig.  54. 

Crown  wheels  have 
their  teeth  parallel 
with  their  axes,  as 


, 

wheel  shown  in  this 
figure  is  called  a  lan- 
tern. 

Bevel  wheels  have 

Fio.  56.  , 

their    teeth    oblique 
to  their  axes,  as  in  Fig.  56. 

181.  Wheels  are  also  connected  by  endless  bands,  as  in 
Fig.  57.  In  this  case,  the  motion  is  communicated  by  the 
friction  of  the  bands  on  the  circumferences  of  the  wheels. 

The  whirling  ta- 
ble, Fig.  93,  con- 
sists of  two  wheels 
thus  connected;  on 
tn  i-ii  ing  the  large 
wheel  around  once, 
the  smaller  is  made 
to  revolve  as  many 
times  as  its  circum- 
ference is  contained 
in  the  circumference 
of  the  larger.  It 
i-  ii-ed  to  give  great 


speed  to  the  axis  of  tin-  smaller  wheel. 

182.  The  pulley.     If  a    e,,,d.    fastened   at  one  end  to  a 


THE   PULLEY. 


89 


FIG.  58. 


hook,  supports  a  weight  at  the  other  end,  it  is  manifest  that 
the  stretching,  or  tension,  of  the  cord  will  be  transmitted 
throughout  its  whole  length,  and  exert  a  force  on  the  hook 
equal  to  the  load.  If,  now,  the  cord  be  passed  over  the 
hook  and  one  end  held  by  the  hand,  the  tension  of  the 
cord  will  remain  the  same,  and  the 
hand  must  exert  a  force  equal  to  the 
load.  No  mechanical  advantage  will 
be  gained  in  raising  the  load  in  this 
manner,  beyond  a  change  in  the  direc- 
tion of  the  power.  In  fact,  there  will 
be  a  loss,  resulting  from  the  friction 
of  the  cord  upon  the  hook.  We  may 
diminish  the  friction,  by  passing  the 
cord  over  a  wheel  revolving  on  the 
hook  as  its  axis,  but  can  not  lessen  the  tension  of  the  rope. 
Such  a  wheel  is  called  the  sheave  of  a  pulley. 

A  pulley  is  a  small   grooved  wheel,  revolving  about  an 
axis,  and  having  a  cord  passing  over  its  circumference. 

Pulleys  are  called  fixed  or  movable,  according  as  their 
axes  are  fixed  or  movable. 

183.  In  the  use  of  the  fixed  pulley  there  is  neither  gain 
nor  loss  to  the  power,  but  only  a  change  in  its  direction. 
This  is  often  as  great  an  advan- 
tage as  an  increase  of  the  power 
would  be.  Thus,  if  a  fixed  pul- 
ley be  attached  to  the  rafter  of  a 
warehouse,  a  man  standing  on 
the  ground  may  raise  weights  to 
any  floor  of  the  building.  It  is, 
besides,  so  much  easier  for  him 
to  pull  the  rope  down  than  it 
would  be  to  lift  the  weight  di- 
ivrtly  up.  that  he  can  afford  to  overcome  the  friction  of  the 
pullry  in  addition  to  the  load.  By  the  use  of  two  fixed 
pulleys,  horizontal  motion  may  be  converted  into  vertical, 
as  in  Fig.  59. 


FIG.  59. 


90 


NATURAL    PHILOSOPHY. 


184.  Movable  pulley.     If  a  cord  be  attached  at  each  end 
to  a  hook,  and  a  weight  hung  by  a  ring  at  the  center  of  the 
*  r    .      cord,  the  tension  of  the  cord  will 

be  transmitted  throughout  its 
length.  If  we  suppose  the  cord 
to  be  divided  into  two  parts,  each 
part  will  support  but  half  the 
load,  and,  therefore,  have  but 
half  the  tension.  Therefore,  if  a 
fixed  pulley  take  the  place  of  one  of  the  hooks,  the  power 
required  to  support  the  load  will  be  one-half  the  weight  of 
the  load.  If  it  is  desired  to  elevate  the  load,  the  friction 
may  he  diminished  by  substituting  a  movable  pulley  for  the 
ring.  Fig.  61. 


FIG.  «o. 


If  one  end  of  the  cord  be  attached  to  the  top  of  the 
movable  pulley,  as  in  Fig.  62,  the  tension  of  the  cord 
produced  by  the  load  will  be  distributed  in  three  equal 
portions.  Consequently,  the  tension  of  the  part  attached 
to  the  power  will  he  measured  by  one-third  of  the  load, 
and  the  combination  will  he  in  equilibrium  when  the  power 
is  one-third  of  the  load. 


SPANISH  BURTONS. 


91 


In  the  arrangement  of  Fig.  63,  the  power  is  one-fourth 
of  the  load.  In  this,  there  are  two  fixed  and  two  movable 
pulleys,  each  pair  secured  in  a  framework  called  a  block.  A 
combination  of  blocks,  sheaves,  and  ropes  is  called  a  tackle. 

185.  As  fixed  pulleys  do  not  increase  power,  the  gain  in 
the  last  three  examples  must  be  due  to  the  division  of  the 
tension  among  the  parts  of  the  rope  supporting  the  movable 
block.  Hence,  representing  the  number  of  these  parts 
by  n, 


[15.]     L  = 


[16.]     P  =  - 
n 


STATICAL  LAW. — The  load  equals  the  power  multiplied  by 
tie  i (limber  of  parts  of  the  cord  engaged  in  supporting  the 
movable  block. 

186.  This  law  applies  only  when  one  continuous  cord  passes 
through  the  whole  system,  and  when  its  parts  are  parallel.     Movable 
pulleys  are  very  seldom  used  alone ;   they   are  generally  combined 
with  fixed  pulleys  which  serve  to  change  the  direction  of  the  power. 
These  combinations   may   contain    from    one  to   ten 

pulleys  in  each  block.  When  the  fixed  and  mov- 
able pulleys  are  equal  in  number,  the  parts  of  the 
string  supporting  the  load  will  be  twice  the  number 
of  movable  pulleys,  as  in  Figs.  61  and  63. 

187.  Spanish  burtons  are   pulleys  contain- 
ing more  than  one  rope.     Such  a  system,  with 
two   ropes,    is  represented   in   Fig.    64.     The 
rope,   P  B  A  D,    sustains   a   tension  equal   to 
the  power;    consequently,  the  portions,  A  B, 
A  D,  each  have  a  tension  equal  to  the  power. 
The  rope,  A  C  B,  sustains  the  tensions,  A  B 
and    B  P,   and,    therefore,    has    a   tension   of 
twice  the  power.      Therefore,  the  united  ten- 
sions  of   the   ropes   supporting    the    movable 
block,  A,  will  be  four  times  the  power. 

In  Fig.  65,  each  pulley  has  a  separate  rope.     The  pulley, 


FIG.  64. 


92 


NA  T  URA  L    PHIL  OS  OP  11 Y. 


B,  receives  half  the  load  attached  to  A,  C  half  of  B,  and  so 
on;  hence  the  power  increases  by  the  geometrical  ratio  of 
8421  2  2.  Therefore,  the  load  will  equal  the 

product  of  the  power  multiplied  by 
'2  used  us  a  factor  as  many  times  as 
there  are  movable  pulleys. 

Although  the  power  increases  rapidly  by 
this  system,  yet  it  is  practically  of  little 
value  because  of  its  limited  range.  In 
the  common  system,  the  motion  may  be 
continued  until  the  fixed  and  movable 
blocks  come  in  contact;  but  in  this  system, 
only  until  D  and  E  come  together,  at  which 
time  the  other  pulleys  will  be  far  apart, 
because  C  rises  halt'  as  last  as  D,  B  one-fourth 
and  A  one-eighth  as  last. 

188.  The  inclined  plane  is  a  hard, 
smooth,  inflexible  surface,  inclined 
obliquely  to  the  resistance.  When  a  weight  is  placed  upon 
such  a  plane,  a  part  of  the  pressure  is  resisted  by  the 


FIG.  66. 


plane,  while   the   remainder  tends  to  cause  the  weight  to 

>lid»-  or  roll  down  the  piano.  Thus,  in  Figs.  66,  67,  and 
(>.s,  the  weight  of  the  body  lies  in  the  line  of  direction  of 
L-ravity,  L  G.  This  may  be  resolved  into  two  components, 
vi/,. :  L  N.  acting  perpendicularly  to  the  plane,  and  com- 
pletely resisted  by  it,  and  L  K,  acting  opposite  to  the 

direction   of  the   power,  and   to  be  counterbalanced   by  it. 

It  i-  manifest  that  the  component,  L  N,  shows  how  much 
of  the  weight  is  supported  by  the  plane.  If  the  plane  were 
vertical,  L  N  would  be  zero,  and  if  the  plane  were  hori- 


THE  INCLINED  PLANE. 


93 


zontal,  the  whole  weight  would  be  supported  by  it.  Con- 
sequently, the  other  component,  L  E,  which  represents  the 
power  necessary  to  sustain  the 
load,  will  increase  as  the  plane 
becomes  steeper.  It  is  also 
manifest  that  this  component, 
L  E,  will  vary  with  the  direc- 
tion of  the  power.  There  may 
be  three  cases. 


FIG.  68. 


189.  In  the  first  case  the 
power  acts  parallel  with  the 
plane,  as  in  Fig.  66.  In  the 
parallelogram,  E  L  N  G,  the  sides  L  G  and  E  N  are  equal; 
hence,  E  N  may  be  taken  as  the  weight  of  the  body,  or 
load.  The  triangles,  ABC  and  L  E  N,  are  similar,  and 
hence, 

Power  :  load  : :  L  E  :  E  N;  or,  : :  B  C  :  A  C. 


[17.]     P  = 


LXBC 
AC. 


[18.]    L  = 


PXAC 
BC. 


STATICAL  LAW. — The  power  equals  the  load  multiplied  by 
the  ratio  of  the  vertical  height  of  the  plane  to  its  length. 

EXAMPLE. — The  power  required  to  keep  a  barrel,  weighing  two 
hundred  pounds,  on  a  plank  twelve  feet  long,  with  one  end  on  the 
ground  and  the  other  in  a  wagon  three  feet  high,  will  be  fifty 
pounds. 

This  is  the  most  advantageous  way  of  applying  the  power,  for  its 
whole  effect  is  expended  in  raising  the  load.  If  the  power  be  directed 
below  the  plane,  a  part  of  it  will  be  expended  in  increasing  the 
pressure  on  the  plane;  and,  if  directed  above  the  plane,  a  part  of  the 
power  will  be  used  in  diminishing  the  pressure ;  and  hence,  only  the 
i'emaining  part  is  available  in  drawing  the  load  up  the  plane.  That 
is  to  say,  in  all  other  cases  a  greater  power  will  be  required  to  raise 
the  same  load. 

190.  In  the  second  case  the  power  acts  parallel  with  the 
base,  as  in  Fig.  67.  The  triangles,  L  E  N  and  L  N  G,  are 
each  similar  to  ABC,  and  we  shall  find, 


94  NATURAL  PHILOSOPHY. 

Power  :  load  :  :  L  E  :  E  N  ;  or,   :  :  B  C  :  A  B. 


[19.]     P  =  [20.]     L 

AB.  BC. 

STATICAL  LAW.  —  The  power  equals  the  load  multiplied  by 
the  ratio  of  tfie  vertical  height,  of  the  plane  to  its  base. 

191,  Third  case.     In  any  other  direction  of  the  power, 
the  triangles  formed  will    not    be   similar,   and   no  simple 
expression  of  equilibrium  can  be  given,  beyond  the  general 
law  of  (157.)  * 

192.  Familiar  examples.      The  grandest  examples  are  found 
in  roads,  which  are  seldom  perfectly  level.     In  ascending  mountains 
the  roads  wind  about,  so  as  to  increase  the  length  of  the  incline.     So, 
also,  a  careful  driver,  in  ascending  a  steep  hill,  -will  guide  his  team  from 
side  to  side  of  the  road,  preferring  to  increase  his  distance  for  the 
sake   of   lightening    his  load.     On    a   level   road,   the   power  of  the 
horses  is  expended  in  overcoming  friction,  which,  on  common  roads, 
varies  from  one  eighteenth   to   one  fiftieth  of  the  load,  and  on  iron 
railways,  from   one    one-hundred-and-fortieth   to  one   two-hundredth. 
On  a  road  rising  one  twentieth,  that  is  one  foot  in  twenty,  the  horse 
must  lift  one  twentieth  of  the  load  besides  overcoming  friction.     Beck- 
oning friction  at  one  eighteenth,  the  whole  power  (jV  +  fV)  necessary 
will  be  almost  double  that  required  on  a  level  road.     On  a  railway, 
with  the  same  grade,  the  power  required  will   increase  from  T^  to 
TOT  +  ^  =  Tftf>  or  eight  times  that  required  on  a  level.     This  rapid 
increase  indicates  the  reason  why  steep  planes  are  less  admissible  on 
railways  than  on  common  highways. 


*The  general  proportion  for  inclined  planes  is  P  :  L  : :  sine  of  in- 
clination of  the  plane  :  cosine  of  the  angle  formed  by  the  direction 
of  the  power  and  the  plane.  Suppose  the  weight  to  be  concentrated 
in  the  point  L,  and  the  line  A  C  to  pass  through  it;  then, 

I •'!-.  08.     P  :  L  ::  sine  BAG  :  cos.  CLE. 

In  Fiir.  '.'..     Cot.  CLE  — radius  /.  P  :  L  : :  sine  BAG  :  1. 

In  Fig.  67.  CLE^  IJAC.-md  is  the  compli-im-nt  of  K  L  N;  hence, 
1'  :  L  ::  siiu-  BACj  <  <  .  I:  \  C. 

The  method  l>y  construction  may  al.so  be  applied.     (125.) 


THE    WEDGE. 


95 


193.  The  wedge  is  a  movable  inclined  plane.  If,  instead 
of  moving  the  weight  along  the  inclined  plane,  Fig.  67, 
the  plane  had  been  pushed  under  the  load,  the  same  advan- 
tage would  have  been  gained.  Therefore,  since  in  the 
wedge  the  power  is  always  exerted  parallel  to  the  base, 

P  :  L  ::  BC  :  A  B. 


[21.]     P=^ 

AB. 


[22.]    L  = 


PXAB 
BC. 


FIG.  69. 


STATICAL  LAW. — The  power  is  to  the  load  as  the  height 
of  the  wedge  is  to  its  base. 

194.  As  commonly  applied  for  sepa- 
rating surfaces,  a  double  wedge  is  used,  as 
A  C  A'  in  Fig.  69.     As  each  face  meets 
with  half  the  resistance,  the  power  is  to 
the  resistance  as  half  the  thickness  of 
the  wedge  is  to  the  length,  B  C. 

195.  These  laws  are  of  little  practical 
value,  beyond  the  general  deduction  that 

the  efficiency  of  the  power  increases  with  the  thinness  of 
the  wedge.     The  reasons  for  this  are : 

1.  The   power  is   applied,  not   by  a  continuous   force   or 
pressure,  but  by  percussion,  for  which  we  have  no  numerical 
standard  of  comparison. 

2.  The    surfaces    to    be    separated    generally   assist   the 
action   of   the   wedge,    by  their   elasticity,  at  the   moment 
of  impact,  and,  frequently,  by  the  leverage  of  the  faces  to 
be  cleft, 

3.  The  value  of  the  wedge  is  often   dependent  entirely 
upon  friction,  as  is  the  case  with  nails,  pins,  and   the  key- 
stones of  arches.     If  it  were  not  for  friction,   the  wedge 
would  recoil  after  every  blow. 

196.  Practical  applications.      The  wedge  is  especially  useful 
where  very   great   force   is  to  be  exerted   through  very  small   space. 
Masses  of  timber  and  stone  are  cleft  by  wedges.     Ships  are  raised  by 


96 


NATURAL   PHILOSOPHY. 


FIG.  70. 


wedges  driven  under  their  keels.  The  most  extensive  application  of 
the  wedge  is  in  tools  for  catting  and  piercing,  as  knives,  awls,  hatchets, 
chisels,  nails,  etc.  The  angle  varies  with  the  purpose  for  which  the 
instrument  is  designed.  Although  the  mechanical  power  is  increased 
by  diminishing  the  angle,  yet  the  strength  of  the  tool  is  diminished  in 
the  same  proportion.  Accordingly,  in  tools  used  for  cutting  wood,  the 
angle  is  about  30° ;  for  iron,  from  50°  to  60° ;  for  brass,  80°  to  90°. 

197.  The  screw  is  another  variety  of  the  inclined  plane, 
as  may  be  shown  by  winding  a  triangular  piece  of  paper 
around  a  cylinder.  Fig.  70.  The 
hypotenuse  will  form  a  spiral  path 
about  the  cylinder  exactly  resem- 
bling the  threads  of  a  screw.  The 
ratio  of  the  base,  AB,  to  the  cir- 
cumference of  the  cylinder,  will 
determine  the  number  of  turns  the 
triangle  will  make,  and,  by  conse- 
quence, the  number  of  parts  into  which  the  height,  OB, 
will  l)o  divided.  Each  of  these  parts,  as  be,  corresponds 
to  the  vertical  distance  between  the  threads  of  the  screw. 
As  in  the  wredge,  the  power  acts  parallel  with  the  base;  the 
action  of  the  screw  is,  therefore,  the  same  as  the  second 
case  of  the  inclined  plane;  hence, 

STATICAL  LAW. — TJie  power  is  to  the  load  as  the  vertical 
distance  between  two  adjoining  threads  is  to  the  circumference 
of  the  screw. 

198.  In  actual  practice,  the 

screw  consists  of  two  parts: 
(1.)  a  convex  grooved  cylinder, 
or  screw,  S,  which  turns  within 
(2.)  a  hollow  cylinder,  or  nut, 
N,  whose  concave  surface  is  cut 
witli  a  thread  exactly  corre- 
spondinir  to  the  threads  of  the 
screw.  The  power  is  employed 
either  to  turn  the  -crew  within 
an  immovable  nut,  or  to  turn  the  nut  about  a  fixed  screw. 


THE  DIFFERENTIAL   SCREW.  97 

In  either  case,  it  is  generally  found  convenient  to  apply  the 
power  at  the  end  of  a  lever,  fitted  either  to  the  screw  or 
to  the  nut.  This  renders  the  contrivance  a  compound 
machine,  whose  advantage  may  be  found  by  the  following 

STATICAL  LAW. — The  power  is  to  the  load  as  the  vertical 
'Usance  between  two  contiguous  threads  is  to  the  circumference 
described  by  the  power. 

P  :  L  ::  be  :  2*R;  or,  ::  be  :  6.2832  FP. 

[23.]     P  =      LX61_  [24]     L -,PX  6.2832 FP 

6.2832  F P.  be. 

EXAMPLE. — If  the  threads  of  the  screw  are  one  inch  apart,  and 
the  lever  is  four  feet  long,  a  power  of  one  pound  will  exert  a  pressure 
of  301.6  pounds. 

199.  The  mechanical  efficiency  of  the  screw  may  be  in- 
creased by  lengthening  the  lever,  or  by  dimishing  the  dis- 
tance 'between   the   threads;    and,   as  we   may  modify  the 
screw  in  both  these  ways  at  once,  to 
an   indefinite  amount,  the  pressure 
which  may  be  exerted  by  a  screw  is 
limited  only  by  the  strength  of  the 
materials.     To  obviate  the  practical 
difficulty  of   making  the   lever  too 
unwieldy,  or  the  thread  too  delicate, 
John  Hunter  invented  the  differential 
screw.     This  consists  of  the  ordinary         |— ^^^ 
right  handed  screw,  into  the  end  of 
which  works  a  left  handed  screw,  so 

that  the  two  move  in  opposite  directions.  The  distance 
between  the  threads  of  the  second  screw  is  somewhat  less 
than  that  between  the  threads  of  the  first.  This  second 
screw  is  prevented  from  turning  round,  but  may  move  up 
and  down.  On  turning  the  lever  of  the  larger  screw,  it 

twill  descend  through  its   nut,  and,  at  the   same  time,   the 
smaller  screw  will  ascend  within  it;  consequently  the  plate, 
N.  p.  7. 


98 


NATURAL  PHILOSOPHY. 


D,  will  descend  the  difference  between  the  pitch  of  the  two 
threads.  Therefore,  with  the  differential  screw,  the  power 
is  to  the  weight  as  the  difference  of  the  distances  bet  WITH 
the  threads  of  the  two  screws  is  to  the  circumference 
described  by  the  power. 

This  principle  is  employed  in  the  micrometer  screw,  which 
is  an  apparatus  used  to  measure  very  small  distances. 

200.  Practical  applica- 
tions. The  screw  is  used  for 
compressing  cotton,  hay,  and 
goods,  for  expressing  the  juices 
of  plants  and  fruits,  to  raise 
buildings,  to  elevate  grain  and 
water,  to  propel  ships,  and  to 
fasten  securely  the  framework 
of  structures  of  all  kinds.  Fig. 
73,  is  the  ordinary  press  used 
for  copying  letters. 


FIG.  73. 


COMPOUND    MACHINES. 

201.  One  of  the  most  useful  of  these  contrivances,  is  the 
endless  screw,  which  is  so  secured  by  its  shoulders  that  it 

has  no  longitudinal 
motion.  Its  thread 
works  obliquely  into 
the  teeth  of  a  wheel, 
which  supplies  the 
place  of  a  nut. 

Ci-anes   and   der- 
ricks   are  combina- 
tions  of  pulleys  with 
a    wheel    and    axle. 
Fl0-74-  One    form    of    the 

crane  is  shown  in  Fi«_r.  7.">.  This  contains  the  wheel  and 
axle,  G,  two  fixed  pulleys,  E  and  F,  and  one  movable 
pulley,  P.  The  vertical  axis,  A,  is  supported  by  suitable 
framework. 


HUMAN  MECHANISM. 


99 


The  power  of  any  compound  machine  may  be  found  by 
estimating  the  effect  of  the  parts  separately,  and  then  com- 
pounding them. 

202.  The  human  mechanism  exhibits  many  examples 
of  simple  machines. 

Thus,  the  nodding  of  the  head  il- 
lustrates a  lever  of  the  first  kind,  in 
which  the  load  is  the  weight  of  the 
head ;  the  fulcrum,  the  atlas  bone,  and 
the  muscles  of  the  neck,  the  power. 
When  a  man  stands  on  his  toes,  the 
floor  is  the  fulcrum,  the  power  is  ap- 
plied at  the  heel  by  the  tendon 
A  chillis,  and  the  weight  of  the  body 
falls  between  the  fulcrum  and  the 
power.  This  is  a  lever  of  the  second 
kind.  We  employ  a  lever  of  the 
third  kind,  in  raising  the  fore-arm 
horizontally.  The  hand,  and  any 
thing  it  contains,  is  the  weight, 
the  elbow-joint  the  fulcrum,  and 
the  power  is  applied  by  a  muscle  attached  to  the  fore-arm,  a  little 
in  front  of  the  joint.  Fig.  76.  In  biting  by  the  front  teeth,  we  em- 
ploy a  lever  of  the 
third  kind.  The  force 
exerted  by  the  muscles 
which  raise  the  lower 
jaw  is  enormous.  In 
man  it  can  not  be  less 
than  three  hundred 
pounds,  and  in  the 
tiger  it  must  exceed 
t\vo  thousand  pounds.  The  muscle  which  directs  the  eye  downward 
and  inward,  passes  through  a  cartilaginous  pulley  attached  to  the 
frontal  bone.  Some  of  the  teeth  are  wedges,  capable  of  cutting  like 
chisels. 

Throughout  the  entire  frame,  we  have  surprising  examples  of  econ- 
omy of  material  to  the  end  designed ;  combining  lightness,  force, 
firmness,  elasticity,  leverage,  motion,  resistance,  security,  and  grace. 
These  contrivances  are  so  numerous,  and  so  wonderfully  constructed, 
that  a  volume  would  be  insufficient  to  describe  them. 


FIG.  75. 


FIG.  76. 


100 


NATURAL   PHILOSOPHY. 


203.  Recapitulation. 

Machines  are  classified  as  simple  and  compound. 
1.  Leverage, 


I.    Simple    machines 
employ 


r  Lever. 

\  Wheel  and  axle. 


2.  Tension  of  ropes.    <  Pulley. 

{Inclined  plane. 
Wedge. 
Screw. 


II.  Machines  are  compounded : 

1.  By  repeating  the  same  simple  machine ;  as  the  compound  lever, 
the  burton,  the  differential  screw. 

2.  By  uniting  two  or  more  simple  machines ;  as  the  endless  screw, 


IMPEDIMENTS    TO    MOTION. 

204.  It  has  already  been  stated  that  power  is  generally 
lost  in  machines  through  rigidity,  and  the  mutual  adhesion 
of  the  materials,  and  the  consequent  diminished  mobility  of 
the  parts  of  the  machinery.  For  this  reason,  the  results 
actually  reached  in  practice  are  somewhat  less  than  those 
determined  by  the  statical  laws.  Therefore,  in  calculating 
the  useful  work  of  any  machine,  due  allowance  should  be 
made  for  the  various  impediments  to  motion.  If  (1.)  the 
purpose  for  which  a  machine  is  designed' is  merely  to  support 
a  load,  the  greater  the  impediments  the  less  will  be  the  power 
required:  but,  (2.)  if  the  object  sought  is  to  move  a  load,  the 
greater  the  impediments  the  greater  will  be  the  power  re- 
quired. 

In  the  first  case,  the  impediments  may  constitute  the 
entire  mechanical  advantage  of  tin-  machine,  as  is  shown  bv 
the  incalculable  utility  of  friction  in  nails  and  screws,  when 
employed  in  holding  different  materials  together.  So,  also, 
friction  is  ncce.-sary  in  almost  every  application  of  power, 
whether  employed  in  simple  motion  or  applied  to  machines. 
Without  friction,  the  wheels  of  a  locomotive  would  turn  on 
the  rails  without  moving  forward,  belts  would  slide  on  their 


FRICTION. 


101 


i 


pulleys  without  starting  them,  all  knots  would  readily 
untie,  and  nearly  all  manufactured  articles  separate  into 
the  parts  of  which  they  are  composed.  In  the  second  case, 
any  impediment  to  motion  is  a  mechanical  disadvantage, 
involving  a  loss  of  power. 

-rC" 205.  Friction  is  termed  sliding,  when  one  surface  slides 
over  another,  as  a  sleigh  upon  ice;  and  rolling,  when  one 
surface  rotates  on  an- 
other, as  a  carriage  wheel 
on  the  ground.  Sliding 
friction  has  been  deter- 
mined for  many  different 
surfaces  by  the  apparatus 
shown  in  Fig.  77.  Blocks 
of  different  materials, 
carrying  varying  weights, 
were  made  to  move  over  various  surfaces,  by  means  of 
weights  placed  in  the  pan,  P.  The  quotient  obtained  by 
dividing  the  force  necessary  to  move  the  body,  by  its  weight 
in  pounds,  is  called  the  coefficient  of  friction.  This  quantity, 
therefore,  represents  the  friction  due  to  the  normal  press- 
ure of  one  pound.  Roll- 
ing friction  is  determined 
by  substituting,  in  place  of 
the  block,  a  cylinder  about 
which  were  placed  cords, 
loaded  at  each  end,  with 
equal  weights,  cc  c'c'. 
The  following  results  have 
been  determined  by  experiments : 


FIG.  77. 


FlQ.  78. 


206.  1.  Friction  increases  with  the  roughness  of  the  surfaces, 
because  a  rough  surface  contains  many  projections  which  fit 
into  corresponding  cavities  of  the  opposing  surface,  and 
these  projections  must  be  either  lifted  out,  bent  down,  or 
broken  off  in  moving. 


102  NATURAL   PHILOSOPHY. 

2.  Rolling  friction  is  less  than  sliding,  because   a  rolling 
motion  avoids  the  breaking  down  of  the  minor  inequalities 
of  the  surface. 

3.  Friction  is  generally  diminished  by  polisliing  the  surfaces, 
and  by  the  interposition  of  unguents,  because  the  projections 
are  smoothed  down  and  the  cavities  are  filled  up. 

4.  Friction  is  greater  between  soft  bodies  than  hard  ones,  be- 
cause soft  bodies  allow  the  opposing  surface  to  sink  some- 
what into  them,  and  thus  increase  the  number  of  particles  to 
be  abraded. 

5.  Friction  is  generally  greater  at  starting  than  after  motion 
has  commenced,   because,   if  either  surface  is   compressible, 
the  contact  becomes   more  intimate  after  a  period  of  rest. 
If  wood  rests  on  wood,  friction  at  starting  attains  its  max- 
imum in  a  few  minutes;    but  when  metals  rest  on  wood, 
the  maximum  intensity  is  not  attained  for  several  days. 

6.  Friction  is  greater  between  surfaces  of  the  same  materials 
than  between  those  of  different    //'//'/>,   because    cohesion    is 
added  to  the  usual  adhesion.     Hence,  it  is  usual  to  make 
axles  of  materials  different  from  those  of  their  supports. 

7.  Friction  is  very  nearly  proportional  to  pressure. 

8.  Friction  is  not  affected  by  extent  of  surface,  except  within 
extreme  limits.     A  brick  will  slide  as  easily  on  its  side  as  on 
its  edge,  because  the  weight  is  distributed  equally  among 
all   points   in    the   surface   on   which   it   rests.      Therefore, 
although  there  are  more  points  in  the  side  than  in  the  edge, 
yet,  as  each  point  in  the  side  receives  a  less  friction  than 
one  in  the  edge,  the  sum  of  the  friction  of  all  the  points 
will  be  the  same. 

Besides  these,  other  factors  of  friction  sometimes  need  to  be  con- 
sidered.    Thus,  in    ordinary   vehicles,  the    inequality   of  the  ground 

and  the  rapidity  of  motion  increase  the  friction  on  hard  ground,  hut 
do  not  on  soft.  The  width  of  the  tire  does  not  ailed  friction  on  hard 
roads,  hut  on  soft  roads  the  friction  i.s  diminished  l.y  the  use  of  broad 
tires.  The  friction  of  carriage  wheels  is  inversely  proportional  to 
the  diameter  of  the  wheel. 


COEFFICIENTS   OF  FRICTION. 


103 


207.    Table  of  Coefficients  of  Friction. 


Materials. 

1    Unctuous 
Without  unguents.        |     surfaces. 

Starting. 

Friction  or  motion. 

Oak  upon  oak   fibers  parallel  

.625 
.540 
.619 
.137 
.194 

.162 

.478 
.324 
.619 
.138 
.194 
.172 
.152 
.217 

.108 
.143 
.085 
.077 
.076 
.075 
.144 
.107 

Oak  upon  oak   fibers  cross  

\Vrous[lit  iron  upon  oak  

Wrought  iron  upon  wrought  iron  . 

Brass  upon  cust  iron  

208.    The  Friction  of  Wagons  on  Lerel  *Roads. 


Loose  sand 0.25 

Common  by-road 0.1 

Dry  highway 0.025 


Macadamized  road 033 

Well  paved  road 014 

Kailroads 0035  to  .0059 


209.  The  rigidity  of  cords,    passing  over  wheels,   also 
occasions  a  loss   of  power  in   transmitting   motion,  which 
varies  with  the  materials  and   the  circumstances  attending 
their  use.     Thus,  it  has  been  found  that  the  loss  due  to 
this  cause  is 

1.  Directly  proportioned  to  the  suspended  weight. 

2.  Directly  proportioned  to  the  diameters  of  the  cords. 

3.  Inversely  proportioned  to  the  diameters  of  the  wheels. 

4.  And  is  greater  in  tarred  than  in  white  ropes,  and  in 
strongly  twisted  ropes  than  in  those  loosely  twisted. 

210.  Resistance  of  fluids.     The  resistance  which  a  moving 
body  encounters  in  air  or  in  water,  is  only  an  effect  of  the 
transference  of  motion.     The  moving  body  constantly  sets 
in  motion  the  particles  of  the  surrounding  fluid,  and  effects 
this  by  the  loss  of  an  equal  amount  of  its  own  motion.     It 
has  been  found  that  the  resistance  of  fluids  to  bodies  mov- 
ing in  them  is  directly  proportioned: 


104  NATURAL  PHILOSOPHY. 

1.  To  the  density  of  the  fluid;  for   the  moving  body  will 
displace  its  own  bulk  of  either  water  or  air;    but  as  the 
water  is  eight  hundred  and  twenty-nine  times  heavier  than 
air,  volume  for  volume,  the  weight  of  the  fluids  displaced 
will    be   exactly  as    their   densities.      The   resistance  of   a 
square  plane,   of  one  foot  area,    moving  in  water  with   a 
velocity  of  one  foot  per  second,  is  0.975  pounds. 

2.  To   ike   square   of  tlie   velocity   of  the   moving   body;    for 
very    swift     motions    the    resistance    increases     even    more 
rapidly.     The  resistance  of  the  air  to  a  cannon-ball,  mov- 
ing with  a  greater  velocity  than  twelve  hundred   feet  per 
second,  is  greater  than  would  be  expected  under  the  law. 
The  increase  seems  to  be  due  to  the  fact  that  air  flows  into 
a  vacuum  at  the  rate  of  twelve  hundred  and  eighty  feet 
per  second,  and,   consequently,  under  very  high  velocities, 
the  ball  is  retarded  not  only  by  the  resistance  of  the  air, 
but  also  by  having  the  pressure  of  the  atmosphere  on  the 
advancing  side  not  counterbalanced  by  the  pressure  on  the 
other. 

3.  To  the  extent  of  surface  of  tJie  moving  body;    for  the 
larger  the  body,  the  greater  will  be  the  mass  of  the  fluid  set 
in  motion  by  it. 

4.  The  form   of  the  surface  also   influences  the  resistance. 
Thus,  if  the  resistance  to  a  given  plane  surface  be  taken  as 
unity,  an  umbrella  of  the  same  area  of  section  at  the  tips 
will  meet  with  almost  double   (1.94)   the   resistance,   when 
the  concave  surface  is  presented  to  the  air;  and  only  about 
three-fourths  the  resistance   (.77),  when   its  convex  surface 
is  presented.     For  this  reason,  the  bows  of  fast  sailing  ves- 
sels are  made  sharp,  so  as  to  divide   the   water  readily.     It 
has  also  been   found  that  the  shape  of  the  .-tern  <>f  a   vessel 
nioditie-   thi-   reH.-tance. 

•").  Large  bodies  encounter  proportionally  fa  r<'.<i.<f<nicc,  than 
small  ones  of  the  same  //';////•<•  //////  <l<  n.<;t//.  In  cannon-balls, 
the  extent  of  surface  meeting  the  n-i>taiice  is  a.-  the  squares 
of  their  diameters;  but  their  weight,  which  is  one  of  the 


RECAPITULATION.  105 

factors  of  their  momentum,  increases  as  the  cubes  of  their 
diameters.  Thus,  if  two  balls  have  their  diameters  in  the 
ratio  of  one  to  two,  the  area  of  resistance  will  be  as  one  to 
four,  but  if  their  velocities  are  the  same,  their  power  to 
overcome  resistance  will  be  as  one  to  eight. 

6.  Bodies  of  the  same  figure  and  volume,  moving  freely 
within  a  fluid,  will  be  enabled  to  overcome  resistance  in  pro- 
portion to  the  square  root  of  their  density.  Balls,  one-fourth 
of  an  inch  in  diameter,  falling  through  the  air,  will  soon 
reach  the  limit  of  accelerated  velocity,  through  the  resistance 
of  the  air,  and  will  attain  a  final  velocity  as  follows:  lead, 
one  hundred  and  eighteen  feet  per  second ;  water,  thirty-six 
feet;  cork,  eighteen  feet. 

211.  The  useful  effect  of  a  machine,  is  that  fraction  of 
the  power  which  is  applied  to  its  proper  work  after  over- 
coming the  various  impediments  to  motion.  As  no  two 
machines  are  exactly  alike,  the  fraction  which  expresses  the 
average  work  is  not  likely  to  be  exactly  applicable  in  any 
special  case.  Nevertheless,  the  following  table  will  give 
some  general  idea  of 

The  Useful  effect  of  Machines. 


Lever 98 

Wheel  and  axle 90 

Pulley 40  to     .80 

Endless  screw 50 


Chain  pump 50 

Undershot  wheel 27  to     .45 

Breast  wheel 45  to     .65 

Overshot  wheel 60  to     .80 


Screw  press 33  j  Turbine  wheel 60  to     .90 

212.  Recapitulation. 

The  useful  effect  of  machines  is  lost, 

(1.)  Either  within  the  machine  itself;  or, 

(2.)  By  external  impediments. 
The  impediments  to  motion  may  be  classified : 

1.  Friction,  either  internal  or  external. 

2.  Rigidity  of  cords  and  belts. 

3.  Resistance  of  fluids. 


106  NATURAL  PHILOSOPHY. 

DYNAMICS. 

213.  Gravitation.     We  have  learned  (1.)  that  the  force 
of  gravitation  tends  to  make  all  bodies  approach  each  other; 
(2.)  that,  for  our  globe,  the  direction  of  gravity  is  toward 
the  earth's  center,  and  (3.)  that  the  point  of  application  is 
at  the  center  of  gravity  of  the  body.     If  we  attach   to  a 
spring  balance,  balls  of  the  same  material  but  of  different 
size,  the  tension  of  the  spring,  due  to  the  force  of  gravity 
acting  on  the  balls,  will  be  proportional  to  the  number  of 
particles  in  each  ball. 

If  two  of  these  balls  be  dropped  from  a  height,  they  will 
reach  the  ground  in  very  nearly  the  same  time,  although 
the  resistance  of  the  air  is  slightly  in  favor  of  the  larger 
ball.  If  the  balls  were  of  the  same  weight  but 
of  different  material,  as  lead  and  cork,  the 
difference  in  bulk  would  cause  so  great  a  differ- 
ence in  the  resistance  of  the  air,  as  to  make 
the  cork  fall  perceptibly  slower. 

If,  however,    any  two  bodies  whatever,   as  a 
bullet  and  a  feather,  be  allowed  to  fall  through 
a  perfect  vacuum,  they  will  reach  the  ground  at 
exactly  the  same  time.     Therefore,  (4.)  gravity 
acts  with  equal   intensity  on   every  particle  of 
matter,    and    (5.)    is    measured  by  the  weight, 
which  is  proportional  to  the  quantity  of  matter. 
Now,  if  we  catch  balls  dropped  from  different 
heights,  we  shall  find  that  the  swiftest  balls  are 
those    which    have   fallen   through    the   greatest 
spaces,    thus   showing  that  the  motion  is  accel- 
erating, and  if  this  experiment   could  be   con- 
ducted in   a  vacuum,   we  should  find  that  the 
increase  of  velocity  is  uniform,  which  proves  (6.)  that  for 
bodies  near  the  surface  of  the  earth,  gravity  is  a  constant 
force. 

214.  The  velocity  attained  by  bodies  falling  freely  through 
the  air,  increa.se.s  so  rapidly  that  it  is  a  difficult  matter  to 


FALLING  BODIES.  107 

determine  with  precision  the  spaces  passed  over  in  successive 
seconds.  GALILEO  determined  the  laws  of  falling  bodies, 
by  rolling  very  smooth  balls  down  a  polished  groove  cut  in  a 
plane,  which  he  inclined  at  different  angles  of  elevation. 

In  the  study  of  the  inclined  plane,  we  learned  that  the 
weight,  or  gravity,  of  any  body  resting  upon  it,  is  resolvable 
into  two  portions,  one  producing  pressure  on  the  surface, 
and  the  other  tending  to  produce  motion  down  the  plane. 
As  this  latter  portion  bears  the  same  ratio  to  the  whole 
force  of  gravity  as  the  height  of  the  plane  does  to  its 
length,  we  may  diminish  it  at  pleasure  by  lowering  the 
height.  We  shall  thus  diminish  the  initial  velocity,  so  as 
to  make  the  motion  slow  enough  to  be  accurately  measured. 
Nevertheless,  as  this  ratio  is  invariable  for  the  same  plane, 
only  the  absolute  motior  will  be  changed.  The  motion  of 
the  body  will  be  accelerated  by  the  same  law  of  constant 
forces,  and  pass,  in  successive  moments,  through  spaces 
bearing  the  same  ratio  to  each  other  as  if  it  fell  freely 
through  the  air. 

215.  To  repeat  the  experiment  of  Galileo,  stretch  two 
parallel  wires  between  the  walls  of  a  room,  at  any  con- 


FIG.  80. 


venient  angle,  as  in  Fig.  80.  On  the  lower  ware  hang  a 
pulley  with  a  weight  suspended  beneath  it,  and  on  the 
upper  wire  fasten  any  convenient  index,  as  a  bell,  or  slip 


108  NATURAL  PHILOSOPHY. 

of  paper,  to  be  moved  by  the  top  of  the  pulley,  b.  Sup- 
pose the  angle  of  inclination  of  the  wire  to  be  such  that, 
in  the  first  second,  it  passes  over  the  space,  as;  in  two  sec- 
onds it  will  pass  over  the  space,  as' ;  in  three,  as",  and  so  on. 
If,  now,  we  measure  these  spaces  we  shall  find  that  the 
spaces  passed  over  in  each  successive  second,  viz.:  as,  ss', 
s' s",  etc.,  increase  in  the  order  of  the  series  of  odd  numbers, 
1,  3,  5,  7,  etc.,  or  at  the  rate  of  two  spaces  for  each  second. 
This  law  of  increase  is  a  direct  consequence  from  the  nature 
of  constant  forces.  For,  as  gravity  may  be  considered  as 
exerted  in  an  infinite  number  of  equal  successive  impulses, 
the  final  velocity,  at  the  end  of  any  second,  will  be  due  to 
the  aggregate  of  all  the  impulses  during  the  whole  time  of 
fall.  Hence,  the  average  velocity  will  be  that  at  the  middle 
of  the  interval  during  which  it  falls,  and  the  final  velocity 
will  be  double  the  average  velocity. 

216.  The  average  velocity  of  the  first  second  carried  the 
pulley  over  the  space,  as,  and  the  final  velocity  is  double 
the  space,  a  s.  Therefore,  if  gravity  were  now  to  cease  to 
act,  the  velocity  already  acquired  will  be  sufficient  to  carry 
the  body  in  the  next,  and  each  succeeding  second,  through 
twice  the  space,  as.  But  during  the  next  second,  the  fresh 
impulse  of  gravity  will  carry  the  body  over  a  space  equal 
to  as;  consequently,  in  the  second  second,  the  body  will 
pass  over  three  spaces,  each  equal  to  as,  or  s  sf  —  3  a  s,  as 
determined  by  experiment. 

In  two  seconds  the  body  will  have  passed  over  a  s',  which 
is  equal  to  1  +  3  =  4  spaces,  and,  as  before,  its  final 
velocity  will  be  double  its  average  velocity.  Since  it  has 
moved  four  spaces  in  two  seconds,  in  the  next  two  its 
acquired  velocity  would  carry  it  over  eight  spaces,  which  is 
the  same  as  a  velocity  of  four  spaces  for  one  second.  But 
as  gravity  adds  a  new  increment  at  each  second,  it  will 
traverse  4+1=5  spaces  in  the  third  second,  and  will 
have  descended,  in  three  seconds,  through  a#",  which  equals 
1  +  3  +  5  =  9  times  the  .-pace,  //  &  The  final  velocity  will 


FALLING   BODIES,  109 


be  9  X  2-i-3=6  spaces.  By  similar  reasoning,  the  body  will 
be  found  to  pass  over  seven  spaces  during  the  fourth  sec- 
ond, and  to  have  fallen  through  sixteen  spaces  at  the  end 
of  the  fourth  second,  and  so  on. 

217.  We  may  express  these  results  by  the  following  table, 
wherein  t  represents  the  number  of  seconds  in  any  given 
time  of  fall.     The  last  term  in  each  series  is  merely  a  gen- 
eralization of  the  whole,  derived  by  simple  inspection   of 
the  previous  terms  in  each  series. 

Number  of  Spaces  fallen  Velocities  Total  space 

seconds.  each  second.  acquired.  fallen  through. 

1121 
2344 
3569 

4  7  8  16 

5  9  10  25 

6  11  12  36 

t  (2t  —  1)  2<  <2 

It  is  evident  that  these  results  will  always  be  the  same, 
whatever  be  the  inclination  of  the  plane,  or  the  space  passed 
over  during  the  first  second.  If,  in  the  actual  experiment, 
the  height  of  the  plane  had  been  one  foot  and  the  length 
sixteen  feet,  the  pulley  would  have  traversed,  in  the  first 
second,  one  foot,  in  the  second,  three  feet,  in  the  third, 
five  feet,  and  so  on.  Therefore,  a  body  falling  freely 
through  the  air  would  pass,  in  corresponding  time,  through 
sixteen  times  these  spaces ;  or  it  would  fall,  in  the  first 
second,  sixteen  feet,  in  the  second,  forty-eight,  in  the  third, 
eighty,  etc.  * 

218.  It  has  been  determined,  by  careful  experiment,  that 
in  the  latitude  of  New  York,  a  body  will  fall,  in  a  vacuum, 
through  16.08  feet  in  one  second,  and  thereby  acquire  a  final 
velocity  of  32.16  feet.     This  last  value  is  called  the  incre- 


"The  apparatus  devised  by  Atwood  and  by  Morin  will  attain  the  same 
result,  but  as  the  description  of  either  is  of  little  use  without  the  appa- 
ratus, the  simple  method  of  Galileo  has  been  preferred. 


110  NATURAL    PHILOSOPHY. 

ment  of  velocity  due  to  gravity,  and  is  generally  represented 
by  <;  =  32.16  feet.  The  space  passrd  over  during  the  first 
second  is  %g  =  16.08  feet. 

If  we  now  employ  the  constant  -\  <j  for  the  indefinite  term 
"  space,"  used  hitherto,  and  denote  by  s,  the  space  passed 
over  during  any  given  second  ;  by  v,  the  velocity  at  the  end 
of  any  given  second;  and  by  S,  the  total  height  of  the  fall 
at  the  end  of  any  second,  we  may  embody  the  results  of  the 
preceding  table  in  the  following  formulas  and  laws: 

For  bodies  sliding 
For  bodies  falling  freely.  down  inclined  planes. 

[25.]    «  =  i?(2t-l).        [25'.]    .  =  i<K2t-l)|- 
[26.]     v  =  tg.  [26'.]     v  =  tg  ~ 


[27.]    8  =  W*.  [27'.]    8  = 

219.  FIRST  LAW.  —  TJie  space  described  by  a  falling  bodi/,  in 
any  given  second,  is  equal  to  tfie  product  of  twice  tfie  number  of 
seconds  minus  one,  into  the  space  described  the  first  second. 


Thus,  a  body  will  fall,  during  the  ninth  second,  (2X9  —  1)  16.08  = 
273.36  feet. 

SECOND  LAW.  —  TJie  velocity  acquired  by  a  falling  bodij  at  the 
end  of  any  given  second,  is  equal  to  the  j>r<»ln<-f  of  the  nuinlx  r 
of  seconds,  into  twice  the  space  described  the  first  second. 

Thus,  the  velocity  attained  at  the  end  of  the  ninth  second  is 
32.16  X  9  =  289.44  feet. 

Tim:i>  LAW.  —  TJie  total  space  described  by  a  falling  body  «f 
tfie  end  of  any  given  second,  is  equal  to  tfie  product  of  tfie  square 
of  the  number  of  seconds,  into  the  space  dwrihnl  f  lie  first  second. 

Tim-,  tin-  total  fall  during  nine  seconds  is  16.08X81  —  1302.48 
feet. 


220.  Wo  may  combine  the  preceding  formulas  by 
braic  pnin-.-M-s  and  determine  five  other  values  For  each  term, 
some  of  which  may  be  of  service.     Thus,  by  eliminating  t 


FALLING   BODIES. 


Ill 


in  [26.]  and  [27.]  we  find  v*  =  2gS;  or,  [28.]  v  =  \/2g8. 
If  g  be  taken  as  32.16,  [29.]  v  =  8.02  l/&  Therefore,  the 
velocity  acquired  by  any  body  falling  through  a  given  height  is 
equal  to  the  square  root  of  the  Jieight  multiplied  by  8.02.  So, 
also,  from  [27.]  we  find  [30.]  t=V  2S-t-g  which  is  very 
nearly  the  same  as  ]  vS.  The  number  of  seconds  re- 
quired for  a  body  to  fall  through  a  given  space  is  very  nearly 
one-fourth  of  the  square  root  of  the  height,  expressed  in  feet. 

221.  These  formulas  are  also  applicable  for  any  constant 
force  whose  intensity,  g,  may  be   found.     In  any  inclined 
plane,  g  is  diminished,  in  the   ratio  of  the  height  to  the 
length,  and  becomes  gh-^-L      The  total  space,  S,  is  iden- 
tical with  /.      If  these   changes  be  made  in  the  preceding 
formulas,  a  new  series  will  be  found,  applicable  to  bodies  on 
inclined  planes.     Formula  [27'.]  becomes  [31.]  l  =  4tl/  h, 
from  which  we  derive,  [32.]  t  =  I  -=-  4  V  h.    Therefore,  when 
the  heights  of  planes  are  equal,  the  times  of  descent  are  pro- 
portional to  their  length. 

Formula  [28.]  becomes  v  =  V  2  g  h  S  -r- 1.  S  and  I  cancel 
each  other,  and  v  =  V  1gh\  or,  [29V]  0  =  8.02l/T,  a 
formula  identical  with  [29.]  whenever  S  represents  any 
vertical  space.  Therefore: 

222.  The  final  velocity 
of  a  falling  body  is  propor- 
tional only  to  the  vertical 
distance  through  which  it 
falls,  and  is  altogether  in- 
dependent of  the  path  it 
follows.      Thus,    a    body, 
Fig.  81,  starting  from  A, 
will  have  the  same  velocity 
on  reaching  the  level,  6c, 
whether    it    falls    through 

either  of  the  grooves  or  vertically  through  ab.     The  time 


FIG.  81. 


112  NATURAL   PHILOSOPHY. 

of  descent  will  be  shortest  on  the  vertical,  but  on  any  other 
line  than  the  vertical,  on  the  groove  /.  This  curve  is 
known  as  a  cycloid.  In  the  cycloid,  the  curve  falls  more 
rapidly  at  first,  and  the  body  acquires  at  the  start  a  greater 
velocity  than  is  possible  in  the  other  grooves.  Another  cu- 
rious property  of  the  cycloid  is  that  the  body  will  descend 
the  whole  length  of  the  curve  in  the  same  time  as  from  any 
intermediate  point,  as  /. 

223.  If  a  body  is  thrown  downward,  to  the  constant  force 
already  found  must  be  added  the  impulsive  force  given  the 
body.     This  is  proportional  to  the  velocity  imparted  and  the 
time  of  its  action. 

Thus,  if  a  body  be  thrown  downward  with  a  velocity  of  fifty  feet 
per  second,  and  is  three  seconds  in  falling,  gravity  alone  would  carry 
it  32  X  ISjV  =  144  J  feet ;  the  impulse  acting  through  three  seconds 
would  carry  the  body  50X3  =  150  feet,  and  therefore  the  total 
height  of  the  fall  is  144|  -f  150=  294£  feet. 

224.  If  a  body  be  thrown  upward,  the  direction  of  the 
body  is   opposite  to   that  of  gravity,  and   consequently  its 
velocity   will  be  diminished  each   second  by  the    quantity 
g  =  32. 16.     Therefore,  the  time  of  its  rise  will  be  found  by 
dividing  its  original   velocity   by  g,   that   is   t  =  v-i-g,  an 
equation  identical  with  [26.]     Hence,  the  time  of  ascent  is 
the  same  as  that  of  a  descending  body,  having  an  equal 
final  velocity.     From   [29.]  S  =  v2  -v-  64.32,  the  height  in 
feet,  to  which  a  body  ascending  vertically  will  reach,  is  equal 
to  the  square  of  its  velocity  divided  by  64.32. 

225.  The   results   thus   attained   by  theory  are  never  realized   in 

practice,  on  account  of  the  friction  on  inclined  planes,  and  the  resistance 
of  the  air  in  every  0886,  as  ha*  l>een  shown  in  the  previous  section. 

226.  Projectiles.     If  a    body  In-    hurled  in  an   oblique  or 
horizontal  direction,  as  when  a  l»all    is  shot    from  a  cannon, 
the  horizontal  distance,  measured  from  the  point  of  <tartinir 
to  where   it  strikes  the  ground,   is   called   the   random,    or 
range. 


PROJECTILES. 


113 


m 


FIG.  82. 


The  range  of  a  projectile  is  due  to   (1.)  the  force  and 
direction     of    projec-  1234 

tion,  (2.)  the  force 
of  gravity,  and  (3.) 
the  resistance  of  the 
air.  Suppose  a  ball 
to  be  fired  horizon- 
tally, Fig.  82,  its  ve- 
locity, due  to  the  force 
of  projection,  will  be 
uniform,  and  may  be 
represented  by  a  num- 
ber of  equal  spaces,  VI 
set  off  along  A  B.  The 
force  of  gravity  draws  it  vertically  toward  the  earth  with 
accelerated  velocities,  which  may  be  denoted  by  the  unequal 
spaces,  1,  3,  5,  7,  etc.  The  resultant  described  by  these 
two  varying  forces,  will  be  the  curve  A  abed,  which  is  of 
the  kind  called  a  parabola. 

If  the  ball  be  fired  obliquely,  its  path  will  also  be  a 
parabola,  as  represented  in  Fig. 
83.  The  greatest  range  is  ob- 
tained with  an  elevation  of  45°. 
It  will  be  seen  by  inspection, 
that  the  range  is  diminished 
equally  by  equal  deviations  above 
and  below  this  angle,  as  for  20° 
or  70°. 

227.  These    results   are    true 

only  for  bodies  moving  in  a  vacuum.  The  resistance 
of  the  air  always  acts  perpendicularly  to  the  resultant 
already  obtained,  and  with  a  force  so  varying  that,  in  gun- 
nery, the  theoretical  results  are  of  very  little  value.  By 
reason  of  this  resistance,  the  path  of  the  ball  never  rises  so 
high  nor  has  so  wide  a  range  as  the  parabola,  but  is  an 
tmsymmetrical  line,  called  a  ballistic  curve.  For  the  same 

N.  P.  8. 


114  NATURAL    PHILOSOPHY. 

reason,  the   greatest  range  for  swift  motions   is  somewhat 
less  than  40°. 

As  each  force  acts  independently  of  the  other,  it  is  evident 
that  the  ball  shot  horizontally  will  reach  the  earth  in 
exactly  the  same  time  as  if  it  had  been  dropped  ;  and,  if 
fired  obliquely,  in  twice  the  time  required  to  drop  the  ball 
from  the  highest  level  it  attains. 

228.  Universal  gravitation.     Thus  far,  without  sensible 
error,  we  have  considered  gravity  as  a  constant  force;   be- 
cause the  heights  through  which  terrestrial  bodies  ordinarily 
pass   are  insignificant  when  compared  with  the  radius  of 
the  earth,  and  their  distances  may  therefore  be  neglected. 
But  when  we   consider  the  earth's  attraction  upon  remote 
bodies,    or    universal    gravitation    acting    between    distant 
bodies,    we    must    take    into    account    not    only    (1.)    the 
quantity  of  matter,  or  mass,  of  each  body,  but,  also,   (2.) 
the  distance  'between  Hie  centers  of  gravity  of  the  two  bodies. 
The  law  of  gravitation,    discovered  in   1666  by  Sir  Isaac 
Newton,  is  usually  stated  as  follows: 

Every  particle  of  matter  attracts  every  other  particle  with  a 
force  (1.)  directly  proportional  to  its  mass,  and  (2.)  inversely 
proportional  to  Hie  square  of  its  distance. 

Representing  gravitation,  mass,  and  distance  of  any  body 
by  G,  M,  and  D,  and  of  any  other  body  by  the  same 
letters  accented,  the  statement  of  each  portion  of  the  law 
becomes, 

[33.]     G  :  G'  ::  M  :  M'. 
[34.]     G  :  G'  ::  D'2  :  D2;  or, 

[35.]     G  :  G'  ::  M  V*  :  M'D'=  ~  :  ~ 

229.  The  student    will   notice:    1.  That  the  greater   the 
mass  the  greater  the  attractive  force  of  the  body. 

If  the  mass  and  attractive  force  of  the  earth  be  taken  as  unity,  the 
masses  and  attractive  forces  of  other  celestial  bodies  will  he  respect- 


GRA  VITA  TION.  115 

ively:   the  Sun,  314,760;   the  Moon,  .0128;    Mercury,  .065;   Venus, 
.785 ;  Jupiter,  300. 

2.  The  attraction  diminishes  as  the  square  of  the  distance 
increases. 

Thus,  the  sun  is  380  times  farther  from  the  earth  than  our  moon, 
and  by  reason  of  its  distance  exerts  but  (^Y  =  Tiliiro  Part  of  the 
tone-  with  which  the  earth  attracts  the  moon.  Nevertheless,  its 
attractive  force,  due  to  mass,  is  314,760  times  that  of  the  earth ; 
therefore,  the  product  of  these  two  quantities,  or  f£f|£$,  shows  that 
the  sun  actually  exerts  on  the  moon  2i  times  greater  attraction  than 
the  earth  exerts. 

3.  The  attraction  is  mutual. 

The  earth  attracts  the  moon  by  its  mass,  and  the  moon  attracts  the 
earth  by  its  mass.  If  the  earth  and  moon  were  to  fall  together,  the 
moon  would  move  81  times  the  distance  traversed  by  the  earth  be- 
cause its  mass  is  but  ^T  that  of  the  earth.  When  any  body  falls  to 
the  earth,  the  earth  also  falls  toward  it,  but  of  course  passes  through 
an  inconceivably  small  space,  by  reason  of  its  greater  mass. 

230.  Whenever  the  distance  between  any  two  bodies 
varies  to  a  sensible  amount,  gravity  must  be  considered  as 
a  variable  force,  which  may  be  measured  by  taking  as 
unity  the  effect  of  gravity  at  the  earth's  surface,  as  shown 
either  by  a  unit  of  surface  weight,  or  by  the  increment  of 
velocity,  #  =  32.16. 

Tims,  if  a  body  be  taken  1000  miles  above  the  earth's  surface,  it  is 
5000  miles  distant  from  the  center.  The  force  of  gravity  will,  there- 
fore decrease  in  the  ratio  (f{$£)2  =  \l-  At  tnis  distance  a  body  will 
weigh  tf  of  its  surface  weight,  and  acquire  a  velocity  of  |f  of  32.16 
feet,  or  20.6  feet  during  a  fall  of  one  second.  At  a  distance  of  2000  miles 
above  the  surface,  the  weight  will  become  f,  and  <jr  =  14.3  feet.  At 
4000  miles,  weight  =  \  and  g  —  8.02  feet.  At  the  distance  of  the  moon, 
which  is  about  60  times  the  earth's  radius,  the  weight,  considered  with 
reference  only  to  the  earth,  becomes  (W)2  =  y^,  and  g  —  .00892  feet. 
Hence,  were  the  moon  to  fall  toward  the  earth,  it  would  pass,  in  the 
first  second,  over  only  about  -£-$  of  an  inch  (.0534  inch). 

If  the  dimensions  of  the  earth  be  taken  as  unity,  the  relative  gravity 
of  any  heavenly  body  may  be  found  by  dividing  its  mass  by  the  square 
of  its  radius. 


116  NATURAL  PHILOSOPHY. 

231,  Since  the  earth's  equatorial  radius  is  thirteen  and 
one-fourth   miles   longer  than   its    polar   radius,  we  should 
expect  to  find  that   the  force  of  gravity  would  increase  in 
going  from  the  equator  to  the  poles.      Careful  experiments 
have  determined    that  a  body,  on   being  carried  from  the 
equator  to  the  poles,  will  gain  yj?  in  weight.     The  oblate- 
ness  of  the  earth  causes  a  gain  of  -5-^  part;    and  the  rota- 
tion of  the  earth  on  its  axis  causes  a  gain  of  the  remaining 
2W  Part-     Consequently,  the  increment  of  gravity  will  vary 
with  the  latitude,    being   at  the   equator   32.0934  feet;  at 
New   York,    32.166   feet;    at  London,   32.1912;    at  Spitz- 
bergen,  32.2528.     These  facts  could  be  verified  by  attaching 
a  load  to  a  delicate  spring,  and  watching  the  changes  of  the 
spring  on  sailing  from  the  equator  to  Spitzbergen. 

232.  If  a  body  could  be  carried  below  the  surface  of 
the  earth,  it  is  manifest  that  the  portion  of  the  earth  above 
the   body  would   attract   it   from   the   center,    and  thereby 
diminish  the  weight  of  the  body.     If  a  ball  could  be  placed 
in  an  empty  space  at  the  earth's  center,  it  would  be  sus- 
tained there    by  equal    and    opposite    attractions,   and,   of 
course,  would  weigh  nothing.     If  the  earth  were  of  uniform 
density   throughout,   a   mass    one    thousand   miles   from  the 
center  would  weigh  one-fourth  of   the   surface  weight ;    at 
two   thousand  miles,  one-half  the  surface  weight ;    at  three 
thousand  miles,  three-fourths  of  the  surface  weight:   and,  in 
general,  the  weight  of  a  !><><Ji/  In-low  tlie  eartlf*  xurfirr    imu/<l  be 
inversely  proportional  to  its  distance  from  the  surface. 

233.  Recapitulation. 

Gravity  is  a  constant  t'«>rcc  when  ma—  alone  is  taken  into  account, 
hut  is  a  variable  force  when  the  distance  between  two  masses  varies 
-eii-ihlv.  It  art-  as  a  constant  force  on  all  l>o<lies  at  the  same  place 
on  the  earth's  surface,  and  i-  a  factor  in  the  phenomena  of  pressure, 
of  falling  hodie-,  and  of  projectile-.  It  acts  as  a  variable  force  in  the 
phenomena  of  the  heavenly  bodies,  and,  also,  to  a  limited  degree,  in 
ditlerent  phuv.-  on  the  same  meridian  of  the  earth. 


THE  PENDULUM. 


The  intensity  of  gravity  may  l>t>  nu-asim-d  : 
1.  By  the  weight  of  bodies. 

•J.  By  the  increment  of  velocity  of  falling  bodies. 
3.  By  the  vibrations  of  a  pendulum. 
This  last  point  is  a  deduction  from  the  following  section. 

THE    PENDULUM. 

234.  About  the  year  1581,  Galileo  noticed  that  a  lamp, 
swinging  by  a  chain  from  the  ceiling  of  the  cathedral  in 
Pisa,  performed  its  vibrations  in  equal  intervals  of  time. 
This  observation  led  him  to  the  invention  of  the  pendulum. 
It  was  first  employed  in  clocks 
by  Huyghens,  in  1656.  If  a 
heavy  bob,  as  B,  Fig.  84,  be 
suspended  from  a  point,  A,  by 
means  of  a  fine  string,  it  will  be 
at  rest  only  when  in  the  line  of 
the  vertical,  AC.  If  the  bob 
be  raised  to  B,  it  will  tend  to 
move  through  the  curve,  B  C, 

.     T 

precisely   as   a  ball  would   roll 

down  an  inclined  plane  of  the 

same  height,  H  C.     The  force  of  gravity,  B  G,  will  be  par- 

tially resisted  by  the  string,  acting  in  the  line  B  L,  and  the 

remaining  component  of  gravity  will  force  the  ball  in  the 

line  B  T. 

Moving  slowly  at  first,  it  will  gradually  gain  in  velocity, 
and  on  falling  the  whole  height,  H  C,  will  have  acquired 
sufficient  momentum  to  carry  it  very  nearly  to  D,  an  equal 
distance  on  the  other  side  of  the  vertical.  Thence  it  will 
return  toward  B,  to  repeat  the  vibrations,  until  the  resistance 
of  the  air  shall  bring  it  to  rest.  This  pendulum  may  be 
considered  simple,  although  it  is  really  compound. 

A  simple  pendulum  is  conceived  to  be  a  heavy  material 
particle,  suspended  by  a  line  without  wreight,  and  oscillating 
about  a  fixed  point. 


Gf 


T"'  c  i 


O     LN 


118 


NATURAL  PHILOSOPHY. 


235.  The  motion  of  the  pendulum,  from  B  to  D,  or 
from  D  to  B,  is  called  a  vibration  or  oscillation.  The  time 
of  vibration,  is  the  time  occupied  by  the  pendulum  in 
describing  this  arc.  The  amplitude  of  vibration,  is  measured 
by  the  angle  BAG,  or  by  the  arc  B  C,  divided  into  de- 
grees, minutes,  and  seconds.  The  center 
of  suspension,  is  the  point  about  wrhich  the 
pendulum  vibrates.  The  laws  of  the  pen- 
dulum may  be  found,  experimentally,  by 
using  simple  pendulums  of  different  lengths 
and  weights,  as  shown  in  Fig.  85. 

236.  Since  the  vibrations  of  any  given  pen- 
dulum are  caused  by  gravity  alone,  the  time 
of  vibration  will  not  vary  with  the  quantity 
or  quality  of  the  weight  suspended.  Thus, 
if  the  ball  c  be  copper  and  d  wood,  they  will 
vibrate  in  the  same  time.  Neither  will  the 
time  sensibly  vary  if  the  amplitude  of  vibra- 
tion does  not  exceed  certain  limits ;  because 
the  increase  in  the  length  of  the  arc  is  so 
compensated  by  increased  velocity  of  the  fall, 
that  the  same  pendulum  will  describe  an  arc  of  five  de- 
grees in  about  the  time  required  for  an  arc  of  five  minutes. 

237.  The  length  of  the  pendulum  is  a  very  important 
consideration,  for  it  can  be  proved,  mathematically,  that  the 
time  of  vibration  of  a  simple  pendulum  in  a  very  small 
arc,  is  equal  to  the  ratio  of  the  circumference  of  a  circle  to 
its  diameter  (expressed  by  *  =  3.1416)  multiplied  by  the 
time  of  falling  vertically  half  the  length  of  the  pendulum. 

Now,  if  we  make  %l  equal  to  X  in  the  formula  [.'>().] 
t  =  V  2  S -f- </,  we  may  expivss  this  law  more  conveniently 
by  the  formula  :  [30.]  t  *  l  l^-g\  that  is,  the  time  of 
one  vibration  of  any  pendulum  is  equal  to  .'J.I 4 HJ  times 
the  square  root  of  the  quotient  of  the  length  of  the  pen- 
dulum divided  by  the  increment  of  gravity. 


FIG.  85. 


THE  PENDULUM.  119 

238.  If  another  pendulum,  vibrating  in  another  place, 
be  represented  by  the  same  variable  factors  accented,  as 
tf  =  *.  V  I'  -j-  </,  we  may  form  the  proportion, 


VT        17 
-  :  7t  \-/: 


canceling  ft, 


[37.] 


If  the  pendulums  be  taken  in  the  same  place,  g  =  o/,  and 
the  proportion  becomes 

[38.]     t  :  if  ::  1/1  :  VH  '.  or,  t*   :  if2  :  :  I  :  I'. 

FIRST  LAW.  —  The  times  of  vibration  of  any  two  pendulums 
are  proportional  to  tfie  square  roots  of  their  lengths. 

SECOND  LAW.  —  The  lengths  of  any  two  pendulums  are  pro- 
portional to  the  squares  of  their  times  of  vibration. 

At  New  York,  a  pendulum  beating  seconds  is  39.1  inches  long. 
The  length  of  a  two  seconds  pendulum  is  39.1  X  22  =  156.4  inches  : 
of  a  half  seconds  pendulum,  is  39.1  X  (I)2  =  9.77  inches;  of  one 
vibrating  once  in  three-fourths  of  a  second,  is  39.1  X  (I)2  =  22  inches. 

If  1  =  1',  that  is,  if  the  same  pendulum  be  carried  to  dif- 
ferent places,  [37.]  becomes 


[39.]     *:*': 

[40.]     t2  :  If*   ::  g'  :  g. 

THIRD  LAW.  —  The  intensities  of  gravity  at  any  two  places  are 
inversely  proportional  to  tJie  square  of  the  times  of  vibration  of 
the  same  peiidulum. 

Since  the  force  of  gravity  increases  (231)  from  the  equator 
toward  the  poles,  the  same  pendulum  will  vibrate  in  less 
time  in  beinjr  carried  from  the  equator  to  the  poles.  As 
the  number  of  vibrations  in  a  given  time  is  inversely  pro- 


120  NATURAL  PHILOSOPHY. 

portional  to  the  time  occupied  in  one  vibration,  the  in- 
tensity of  gravity  in  any  two  places  will  be  directly  as  the 
squares  of  the  number  of  vibrations  performed  in  a  given 
time  by  the  same  pendulum.  [41.]  g  :  g'  : :  n2  :  n'2. 

239.  If  t  =  £',  that  is,  if  two  pendulums  vibrate  in  the 
same  time  in  different  places, 

[42.]     1:  If  ::  g  :  </. 

FOURTH  LAW. — Tlie  lengths  of  any  two  pendulums  vibrating 
in  the  same  time  are  directly  proportional  to  tiieir  increments 
of  gravity. 

It  follows,  from  this,  that  a  seconds  pendulum  must  be 
lengthened  as  its  distance  from  the  equator  increases.  This 
important  deduction  is  amply  confirmed  by  careful  experi- 
ments, made  in  various  latitudes.  The  length  of  a  seconds 
pendulum,  at  the  level  of  the  sea,  is,  at  the  equator, 
39.02167  inches;  at  New  York,  39.10237  inches;  at  Lon- 
don, 39.13983  inches;  at  Spitsbergen,  39.21614  inches. 

240.  Since  the  length   of  a  seconds  pendulum  can  be 
determined  with   great    accuracy,    we   have   in   it   a    ready 
means   of  determining    the   variation    in   the   intensity   of 
gravity   on  the   earth's   surface,  and,  by  consequence,   can 
calculate  the  figure  of  the  earth,  to  which,  combined  with 
its  rotation,  the  variation  is  due. 

In  the  original  equation,  t=jtV/l^-g,  if  t  equals  one 
second,  g  =  ft2  1  =  9.87  Z.  Hence,  at  New  York,  the  incre- 
ment of  gravity  is  39.10237x9.87=385.94  inches^ 
32.16  feet.  The  fall  of  a  body,  in  vacuo,  at  New  York, 
•  luring  the  first  second,  is  one-half  this  quantity,  or  192.97 
inches. 

241.  These  laws   are   strictly  true  only   when  the  pen- 
dulum vibrates    in    a   ryrloidnl    arc,    or   an    infinitely    small 
circular  arc.      If  two  pendulums  of  the  same  length  vibrate 
in    unequal    ares,  the  one   moving   in  the   shorter   arc   will 
gain    on    the    other.      The    daily    lo.-s    throii-h    increase    in 


THE  PENDULUM.  121 

the  length  of  the  arc  is  equal  to  f  A2,  in  which  A  repre- 
sents the  amplitude,  expressed  in  degrees. 

The  daily  loss  for  an  arc  of  1°  is  If  seconds;  for  4°,  26|  seconds; 
for  6°,  1  minute  ;  for  12°,  4  minutes.  Therefore,  unless  the  arcs  are 
very  unequal,  we  shall  not  be  able  to  detect  any  difference  in  their 
times  of  vibration,  except  after  a  long  interval. 

242.  The  compound  pendulum  usually  consists  of  a  heavy 
boh,  suspended   by  an   inflexible  bar,  from   a  fixed   point. 
In  this,  the  mass  of  the  bob  and  the 

weight  of  the  bar  are  both  to  be  re- 
garded. If  the  motions  of  any  three 
particles  of  the  system,  as  a,  o,  and  b, 
be  considered,  it  is  manifest  that  those 
nearest  the  center  of  suspension  will 
tend  to  move  with  the  greatest  ve- 
locity. Hence,  the  particle  at  a  will 
accelerate  the  more  distant  particles  at 
6,  and  the  more  distant  particles  will 
retard  those  nearer.  There  will,  how-  \o-/ 
ever,  be  one  particle,  as  at  o,  which  $^5"""" 
moves  at  the  average  rate  of  all,  and 
in  which  the  tendency  of  the  particles  FlG-  8&- 

above  it  to  accelerate  its  motion  is  exactly  compensated  by 
the  tendency  of  the  particles  below  it  to  retard  its  motion. 
It  will,  therefore,  move  as  if  it  were  vibrating  alone  by  a 
thread  without  weight,  thus  fulfilling  all  the  conditions  of  a 
simple  pendulum.  If  all  the  matter  of  the  pendulum  were 
concentrated  in  this  particle,  its  rate  of  vibration  would  re- 
main unchanged.  This  point,  which  generally  lies  below 
the  center  of  gravity,  is  called  the  center  of  oscillation. 

243.  The  length  of  a  compound  pendulum  is  the  dis- 
tance  between    the   centers   of  suspension    and   oscillation. 
In   a   uniform   bar,  suspended   from  one  end,  the  center  of 
oscillation  will  lie  two-thirds  of  the  length  of  the  bar  from 
the   center  of  suspension.     The  centers   of  oscillation   and 
suspension   are  mutually   interchangeable.     It  is  this  fact 


W" 

s 


122  NATURAL   PHILOSOPHY. 

which  enables  us  to  determine  the  length  of  a  seconds  pen- 
dulum with  accuracy.  Good  results  may  be  attained  by 
the  following  simple  apparatus.  Fig.  87.  Make 
of  hard  wood  a  slender  bar  about  sixty  inches 
o  long.  Mark  the  position  of  the  center  of  gravity, 
which  should  be  made  to  correspond  very  nearly 
with  the  center  of  the  bar.  About  19.55  inches 

»> 

above  and   below  this   point  insert   two    bits    of 
knitting  needles,  or,  preferably,  knife  edges. 

The  bar,  made  to  swing  from  either  point,  will 
vibrate  in  about  one  second.  If  the  vibrations 
from  the  two  centers  are  not  performed  in  exactly 
the  same  time,  the  bar  may  be  adjusted  by  ele- 
vating  or  depressing  the  center  of  gravity.  This 
may  be  done  by  placing  a  coil  of  fine  wire  about 
the  bar,  where  patient  trial  shall  determine  it  is 
needed.  When  the  times  of  vibration  from  either  point  of 
suspension  are  the  same,  the  distance  between  them  is  the 
length  of  the  pendulum.  If  the  precise  time  of  this  vibra- 
tion is  known,  the  length  of  a  seconds  pendulum  can  be  cal- 
culated. A  shorter  rod  may  be  used  to  attain  the  same  result. 

244.  Suppose  such  a  bar  to  be  suspended  from  S,  and  a 
pound  weight,  W,  to  be  attached  to  the  bar  exactly  at  O  ; 
then,  since  all  the  matter  of  the  pendulum  may  be  considered 
as  concentrated  in  the  center  of  oscillation,  without  regard 
to  the  quantity  of  matter,  any  addition  at  that  point  will 
have  no  influence  on  the  time  of  vibration,  although  the 
bar  will  then  have  a  new  center  of  gravity,  as  at  G'. 

If  this  weight  be  applied  below  the  point  O  at  W,  its  effect 
will  be  not  only  to  depress  the  center  of  gravity,  but  also 
that  of  oscillation,  and  thereby  lengthen  the  pendulum. 

If  the  weight  is  applied  between  S  and  O  at  \V".  its  effect 
will  IM-  to  raise  the  center  of  <rravitv  and  oscillation,  ami 
thereby  shorten  the  pendulum.  Thus  any  addition  of  matter 
made  below  the  point  of  .-u.-pen>ii>n,  except  at  the  center  of 
oscillation,  lengthens  or  shortens  the  pendulum. 


COMPENSATING  PENDULUMS.  123 

245,  If,  now,  the  weight  is  applied  above  the  center  of 
suspension,  at  W",  it  tends  to  retard  the  vibration  of  the 
bar,  because  the  particles  above  S  move  in  exactly  opposite 
directions    from   those   below.      The   time   of  vibration   is 
thereby  lengthened,  and,  consequently,  the  center  of  oscilla- 
tion is  lowered.     We  may  lower  the  center  of  oscillation  to 
any  extent   by  increasing   the  weight,  or  by  increasing  its 
distance  above  S.     Every  successive  addition,  while  it  raises 
the  center  of  gravity,  lowers  the  center  of  oscillation. 

If  sufficient  addition  be  made  above  S,  the  center  of 
gravity  may  be  made  to  coincide  with  the  center  of  suspen- 
sion ;  the  bar  will  be  in  a  state  of  neutral  equilibrium,  and 
if  set  in  motion  will  tend  to  rotate  continually. 

Now,  as  we  can  raise  the  center  of  gravity  as  near  the 
center  of  suspension  as  we  please,  without  making  them  co- 
incide, we  may  so  increase  the  distance  of  the  center  of  oscil- 
lation that  it  shall  be  below  the  bar.  The  bar  may  be  made  to 
vibrate  in  two,  three,  or  even  five  seconds,  which  correspond 
to  the  vibration  of  pendulums  whose  lengths  are  156.4, 
351.9,  and  977.5  inches. 

246,  The  utility  of  a  pendulum,  as  a  measure  of  time, 
depends  upon  the  perfect  equality  in  the  times  of  its  vibra- 
tions.    It  is,  therefore,  essential  that  the  distance  between 
the  centers  of  suspension  and  oscillation   should  be  inva- 
riable.    In  ordinary  clocks,  heat  tends  to  lengthen,  and  cold 
to  shorten,  the  pendulum,  and  hence  such  clocks  are  apt  to 
go  too  slow  in  summer,  and  too  fast  in  winter.     This  ten- 
dency may  be  counteracted  by  raising  the  bob    to  make  the 
clock  go  faster,  and  by  lowering  the  bob   to  make  the  clock 
go  slower. 

247,  Compensating  pendulums  are  those  which  are  made 
self-regulating,  by  constructinir  them  of  two  substances,  in 
such  proportions  that  the  change  in  length  of  one  upward 
is  exactly  compensated  by  an   equal   change  of  the  other 
downward. 


124 


NATURAL  PHILOSOPHY. 


Thus,  the  gridiron  pendulum,  Fig.  88,  consists  of  a  series  of  five 
steel  bars,  expanding  downward,  and  a  series  of  lour  brass  bars,  ex- 
panding upward.  In  this  the  length  of  the  steel 
bars  is  l£-£  that  of  the  brass.  The  mereurial  pen- 
dulum, Fig.  89,  beating  seconds,  lias,  at  the  end 
of  a  steel  rod,  a  stirrup  holding  one  or  two  glass 
cylinders,  each  containing  a  column  of  mercury 
about  6.7  inches  high. 

248.  The  mode  in  which  the  pendulum  is  ap- 
plied to  clocks  is  shown  in  Fig.  89.  The  pendu- 
lum rod  passing  between  the  prongs  of  a  fork,  /, 
communicates  its  motion  to  the  rod,  r,  which 
oscillates  on  a  horizontal  axis,  «.  To  this  axis  is 
fixed  the  escapement,  PP',  terminated  by  two  pro- 
jections, or  pallets,  which  work  alternately  in  the 
teeth  of  the  scape  wheel,  S.  This  wheel,  acted  on 
by  the  weight,  W,  through  a  train  of  wheels  (not 
shown  in  the  figure),  tends  to  move  in  the  direc- 
tion of  the  arrow.  If  the  pendulum  is  at  rest, 
the  wheel  is  held  at  rest  by  the  pallet,  P/,  and 
with  it  all  of  the  clock 
work. 

Now,  if  the  pendulum 
be  moved  to  the  posi- 
tion shown  by  the  dot- 
ted line,  P  is  raised,  and  the  wheel  escapes 
from  the  pallet,  and  the  weight  causes  the 
wheel  to  turn  until  its  motion  is  arrested 
by  the  other  pallet,  P',  which  has  been 
brought  in  contact  with  another  tooth  of  the 
wheel  in  consequence  of  the  motion  of  the 
pendulum.  In  this  manner  the  descent  of 
the  weight,  and  the  consequent  movement 
of  the  clock-work  is  rcgul.-itrd  by  the 
pendulum.  The  faces  of  the  pallets  are 
slightly  incliiu-d.  so  that  each  Moth  of  tin- 
wheel,  Oil  <v-caping,  gives  the  escapement 
a  -IL'lit  im|nil.-e,  which  H  communicated  to 
the  pendulum,  and  compensate-  for  its  loss 
of  motion,  due  to  friction  and  the  resistance  of  the  air. 

249.  If  we  swing  a  simple  pendulum  in  our  fingers,  in 


FIG.  88. 


Fio.  89. 


THE  PENDULUM.  125 

any  direction,  then,  by  virtue  of  the  second  law  of  motion, 
it  will  tend  to  vibrate  in  the  same  direction  incessantly. 
We  may  even  twirl  the  string,  so  as  to  make  the  ball  re- 
volve on  its  axis,  without  altering  the  direction.  In  other 
words,  the  plane  of  vibration  of  a  pendulum  is  invariable,  and 
is  not  affected  by  rotating  the  point  of  suspension. 

Foucault  has  applied  this  principle  in  demonstrating 
the  diurnal  revolution  of  the  earth.  Suppose  a  long  pen- 
dulum were  suspended  over  the  north  pole  and  set  to  vi- 


FiG.  90 


brating  toward  a  given  star,  in  the  line  mm',  it  would  con- 
tinue to  vibrate  in  the  same  direction,  toward  or  from  the 
star.  Meanwhile  the  earth,  revolving  on  its  axis,  would 
bring  a  new  meridian  beneath  the  arc  of  the  pendulum  at 
each  vibration,  and,  as  an  observer  on  the  earth's  surface  is 
unconscious  of  his  own  motion  with  the  earth,  the  pen- 
dulum would  appear  to  move  toward  the  right;  that  is, 
from  east  to  west,  or  in  opposite  direction  from  that  of  the 
earth.  In  twenty-four  hours,  every  meridian  of  the  earth 
would  have  been  brought  beneath  it,  and  hence  the  pen- 
dulum at  the  poles  has  an  apparent  motion  of  fifteen 
degrees  per  hour.  At  the  equator,  the  plane  of  vibration 


126  NATURAL  PHILOSOPHY. 

is  carried  forward  by  the  revolution  of  the  earth,  and, 
therefore,  the  pendulum  will  undergo  no  change,  in  refer- 
ence to  the  direction  of  its  vibration. 

Between  the  equator  and  the  poles,  the  apparent  change 
increases  as  we  recede  from  the  equator,  from  0°  to  15° 
each  hour.  * 

The  experiment  is  best  performed  with  a  long  wire  and  a  very 
heavy  bob.  Foucault  hung  from  the  dome  of  the  Pantheon,  in  Paris, 
a  pendulum  two  hundred  and  twenty  feet  long,  so  as  to  vibrate  over 
a  table,  and  within  a  circular  frame  divided  into  degrees,  minutes, 
and  seconds.  The  path  of  the  pendulum  was  marked  by  means  of 
fine  sand  sprinkled  on  the  table.  The  pendulum,  at  each  double 
vibration,  returned  to  a  point  about  one  hundred  seconds  to  the  left 
of  its  starting  point,  and,  as  the  experiment  was  performed  on  a  large 
scale,  this  motion  could  be  detected  by  the  eye,  and  thus  the  motion 
of  the  earth  on  its  axis  was  rendered  visible. 

250.  If  it  were  required  to  stop  the  motion  of  a  pen- 
dulum instantly,  without  producing  any  pressure  on  the 
center  of  suspension,  the  force  must  be  applied  at  the 
center  of  oscillation.  Hence,  this  point  is  also  called  the 
center  of  percussion,  because  it  is  the  point  in  which  all  the 
impetus  of  a  moving  body  may  be  considered  as  concen- 
trated. The  effect  of  any  blow  given  or  received  at  this 
point  will  be  greater  than  at  any  other.  If  a  stick  of  uni- 
form thickness,  held  at  one  end,  be  twirled  around  by  a 
motion  of  the  wrist,  and  made  to  strike  an  obstacle  at  a 
point  on  the  stick  nearer  or  more  remote  than  two-thirds  of 
its  length,  a  disagreeable  jar  will  be  felt.  The  jar  will  not 
be  noticed  if  the  blow  is  given  at  exactly  the  center  of  per- 
cussion. 

Since  the  centers  of  suspension  and  oscillation,  or  percus- 
sion, are  interchangeable,  if  we  strike  a  Mow  at  one  end  of 
the  stick,  we  shall  avoid  .-train  by  holding  the  rod  at  one- 
third  of  its  length  from  the  other  end.  A  good  ball  or 


*The  hourly  variation  N  propm  i  ional  to  t  lie  sine  of  th>-  Infifmlr  ;  hence, 
at  Cincinnati,  it  should  be  about  nine  degrees  twenty-five  minutes  per 
hour. 


THE  BALLISTIC  PENDULUM. 


127 


cricket  player  soon  learns  by  experience  at  what  point  he  can 
strike  the  most  effective  blow  with  his  bat.  In  axes,  ham- 
mers, etc.,  the  head  is  made  heavy,  so  that  the  centers  of 
gravity  and  percussion  are  very  near  each  other.  As  the 
center  of  oscillation  is  sometimes  outside  of  the  body,  so, 
also,  a  hammer  may  be  so  made,  or  held,  as  to  have  no 
center  of  percussion  within  it.  Such  a  body  will  expend 
part  of  its  impulse  in  a  strain  upon  its  axis. 

251.  A  beautiful  illustration  of  the  center  of  percussion 
is  seen  in  the  ballistic  pendulum,  an  instrument  employed  to 
measure  the  velocity  of  pro- 
jectiles. This  consists  of  a 
heavy  mass  of  wood,  sus- 
pended at  the  end  of  a  long 
iron  bar.  If  a  cannon  ball 
strikes  the  ballistic  pendulum 
at  the  center  of  percussion, 
it  simply  makes  it  swing  like 
a  pendulum ;  but  if  the  im- 
pact is  at  any  other  point,  a 


part   of   the    force    tends    to 

tear  it  away  from  its  axis.  The  velocity  with  which  it 
begins  to  move  when  the  cannon  ball  first  strikes  it,  may 
be  determined  by  observing  the  length  of  the  arc  through 
which  the  mass  is  driven ;  the  weight  of  the  mass  being 
also  known,  the  momentum  and  velocity  of  the  ball  may 
be  calculated. 

252.  Recapitulation. 

The  pendulum  may  be  simple  or  compound. 

The  length  of  a  pendulum  is  the  distance  between  the  centers  of 
suspension  and  oscillation. 

The  time  of  vibration  depends, 

1.  On  the  force  of  gravity. 

2.  On  the  length  of  the  pendulum. 

3.  On  the  amplitude  of  vibration. 


128  NATURAL   PHILOSOPHY. 

CIRCULAR   MOTION. 

253.  Suppose  a  ball  to  be  whirled  in  a  circle,  by  means 
of  a  rubber  cord  held  by  the  hand.     The  ball  will  tend  to 
fly  off,  and  will  exert  a  certain  tension  on  the  cord,  which 
will   be  resisted  by  the  elastic  force  of  the   rubber.      The 
ball  is,  therefore,  revolving  by  reason  of  two  forces,  viz.: 
the  impulse  given  by  the  hand,  and  the  restraining  power 
of  the  cord. 

Circular  motion  is  always  produced  by  the  action  of  two 
forces,  which  are  called  the  centripetal  and  ccntrifinjal  forces. 
The  centripetal  force  acts  along  the  radii  of  the  circle,  and 
tends  to  draw  bodies  toward  the  center.  The  centrifugal 
force  acts  at  right  angles  to  the  radii,  and  tends  to  make 
bodies  fly  farther  from  the  center,  in  the  direction  of  the 
tangent  to  the  circle.  In  the  previous  example,  the  elas- 
ticity of  the  rubber  represents  the  centripetal  force,  and 
the  tension  exerted  by  the  ball,  the  centrifugal  force. 

254.  It  is  only  when  these  forces  are  exactly  equal,  that 
circular  motion  can  be  maintained;  for  if,  at  any  time,  the 
centripetal  force  is  destroyed  by  breaking  the  cord,  the  ball 
will    fly    off  in    a    tangent.       If    the    centrifugal    force    is 
destroyed,  the  cord  will  draw  the  ball  again  to  the  hand. 
If  either  force  were  weakened,  the  ball  would  describe  some 
other  curve  than  a  circle.     If  both  forces  are  increased  or 
diminished  in  the  same  proportion,  the  effect  will  be  merely 
to  increase  or  diminish  the  amount  of  motion. 

255.  If  a  stone  be  hurled  from  a  slin<r,  \ve  may  measure 
cither  force  by  the  momentum   of  the  stone  as  it  leaves  the 
.-trap.      We  ran   readily  determine  that,  when  the  other  far- 
tors  are  unchanged,  the  centrifugal  force  (1.)  will  increase 
with    the   number   of   revolutions    made    in    a    second,    and 
(2.)  also  with   the  weight  of  the  projectile.      A  more  precise 
determination  will  require  a  closer  analysis  <>f  circular  mo- 
tion. 

Suppose    a   body  at   the   point  a,  to  be   under  tin-  influence  <>f  t\\<> 


CIRCULAR   MOTION. 


129 


forces,  viz.:  (1.)  a  constant  force  acting  at  infinitely  small  intervals, 
and  capable  of  moving  the  body  in  the  direction  of  a  fixed  point,  C, 
with  a  force  equal  to  a&;  and  (2.)  an 
impulsive  force  at  right  angles  to  the 
constant  force,  and  represented  both 
in  intensity  and  direction  by  a  d. 
Under  the  joint  action  of  these  forces, 
the  body  will  move  in  the  diagonal 
a.  a',  which  will  also  measure  the  in- 
tensity with  which  it  would  continue 
in  the  same  direction  forever,  were 
the  constant  force  to  cease.  But  the 
constant  force  acts  in  the  second  in- 
stant with  equal  intensity,  o/6/,  to- 
ward the  point  C,  and,  therefore,  the 
line  traced  in  the  second  instant  will  be  a' a".  In  like  manner,  the 
body  will  pass,  in  succeeding  instants,  over  lines  which  form  the 
perimeter  of  the  polygon,  a  a',  a"  a'",  etc.  2s  ow,  as  the  instants  of 
time  considered  are  infinitely  small,  the  perimeter  of  the  polygon 
will  not  differ  from  a  circle  whose  center  is  C. 

To  determine  the  measure  of  these  forces,  we  find,  by 
Geometry  (325),  a  b  :  a  a  ::  a  a'  :  ao;  or,  a  b  =  a  a'2  -r-  a  o; 
but  a  b  represents  the  centripetal  force,  and  its  equal,  the 
centrifugal;  a  a'  represents  the  velocity  of  the  body,  and  ao 
the  diameter  of  the  circle  in  which  it  revolves.  Therefore, 
the  centrifugal  force  equals  the  square  of  the  velocity,  divided 
by  twice  the  radius  of  the  circle  in  which  the  body  revolves : 


[43.]     C  = 


2r 


256.  To  ascertain  the  relation  of  centrifugal  force  to 
gravity,  we  have  only  to  compare  the  spaces  in  feet  through 
which  a  body  would  move  in  a  second  under  gravity  alone, 
and  under  the  centrifugal  force  alone.  Thus,  we  know  that 
a  body  whose  weight,  or  gravity,  is  W,  will  fall  in  one  sec- 
ond £  g  =  16.08  feet.  Hence, 


W_:C  ::* 

N.  P.  9. 


:  or,   [44.]    *-— 


U6  r 


130  NATURAL   PHILOSOPHY. 

That  is,  The  centrifugal  force  of  a  body  is  equal  to  the  prod- 
uct of  its  weight  by  the  square  of  its  velocity  j»  r  wrond  in  feet, 
divided  by  32.16  times  the  radius  of  the  circle  expressed  in  feet. 

257.  A  different  expression  may  be  given  to  this  formula, 
by  employing,  instead  of  velocity  (1.)  the  number  of  sec- 
onds required  to  perform  one  revolution  =tt  or  (2.)  the 
number  of  revolutions  performed  in  one  second  =  n.  Since 
the  circumference  of  a  circle  equals  2  jt  r,  if  v  is  made  to 
represent  the  space  described  in  one  second,  the  number 
of  seconds  required  to  make  one  revolution  is  t  =  2jtr-+-v. 
Whence,  v2  ==  4  *2  r2  -j-  t2  .  Substituting  this  value  in  [44.], 

W      4?i2  r2      Wr      4jt2 
[45.]    0  =      x=x 


Again,  the  velocity  is  the  number  of  revolutions,  or  frac- 
tion of  a  revolution,  made  in  one  second;  or  v  =  2nrn. 
Whence,  v2  =4  ft2  r2n2.  Substituting  this  value  in  [44.], 

W  4rt2 

[46.]  C  =  —  X4*2r2?i2=Wrn2X  —  :=Wrn2Xl.2275. 

The  last  formula  may  be  thus  expressed  :  The  centrifugal 
force  of  a  body  revolving  in  a  circle  is  equal  to  the  product  of 
its  weight  by  the  number  of  feet  in  tJie  radius  of  the  circle,  mul- 
tiplied by  the  product  of  the  square  of  the  number  of  revolutions 
per  second  by  1.2275. 

If,  for  example,  a  sling  two  feet  long  whirl  a  ten  pound  weight  at 
the  rate  of  five  revolutions  per  second,  the  centrifugal  force  is  10  X 
2  X  52  X  1-2275  =  613.75  pounds,  or  it  would  require  that  foree  to  re- 
tain it  in  the  sling.    To  retain  any  weight  in  this  slin<j  at  all  possible 
positions,  the  centrifugal   force  must  equal  gravity,  or  C  =  W,  and 
the  equation  becomes  1  =  rn2  X  1.2275,  from  which  we  find   that  the        , 
.-lin-  -hould  revolve  at  the  rate  of  two-thirds  of  a  revolution  per  sec-       ) 
ond. 

258.  By  the  inspection  of  these  equations,  we  find: 

1.  Tfiat  the  centrifugal  force  increases  with  the  weight. 

2.  Wlien  the  radii  are  equal,  Hie  centrifugal  fanes  are  directly 


CENTRIFUGAL   FORCES. 


131 


as  the  square*  of  the  velocities  per  second,  or  as  the  squares  of 
the  number  of  revolutions  per  second. 

3.  When  the  times  of  revolution  are  equal,  the  centrifugal  foi'ces 
are  directly  as  their  radii. 

4.  The  centrifugal  forces  of  any  two  bodies  are  in  the  com- 
pound ratio  of  their  weights,  their  radii,  and  the  squares  of  their 
velocities. 

259.  These  laws  may  be  fully  verified  by  the  whirling 
table,  Fig.  93.     Thus,  the  first   and   third  may  be  verified 


FIG.  93. 

by  attaching  to  the  axis  of  rotation  a  frame  on  which  a 
wire,  a  b,  is  stretched.  Two  perforated  balls,  united  by  a 
string,  are  placed  on  this  wire,  and  the  frame  is  made  to 
revolve  rapidly.  (1.)  If  the  balls  are  of  unequal  weight 
and  equally  distant  from  the  axis,  the  heavier 
ball  will  draw  the  other  to  its  own  side  of  the 
frame.  (2.)  Unequal  balls  will  remain  at  rest 
if  placed  on  opposite  sides  of  the  axis,  at  dis- 
tances inversely  proportional  to  their  weights. 


Other  apparatus  attached  to  the  table  may  be  used 
to  demonstrate  the  other  laws;  but  as  this  apparatus 
is  not  common,  the  following  examples  are  also  ad- 
duced : 

If  a  glass  bottle,  containing  a  little  colored  water 
and  some  mercury,  is  swiftly  revolved  by  a  twisted 
string,  both  fluids  will  be  whirled  away  from  the  axis, 
but  the  mercury,  having  the  greater  relative  weight,  will  occupy  the 
equator  of  the  bottle,  leaving  a  belt  of  water  on  each  side.  Fig.  94. 
This  confirms  the  first  law.  When  a  circus  rider  drives  into  the 
ring,  he  stands  erect,  that  the  line  of  direction  may  fall  between  his 


132 


NATURAL  PHILOSOPHY. 


feet.  As  he  increases  his  motion  around  the  ring,  the  centrifugal 
force  gives  both  himself  and  his  horse  an  outward  tendency  which 
they  counteract  by  leaning  toward  the  center  of  the  circle.  By  so 
doing,  the  rider  causes  his  line  of  direction  to  fall  without  his  base 
and  within  the  ring,  and  thus  the  resultant  between  the  outward 
action  of  the  centrifugal  force  and  the  downward  action  of  gravity  is 
kept  in  a  line  perpendicular  to  the  circular  bank  around  the  ring. 
As  a  consequence  of  this,  a  less  portion  of  the  weight  of  the  rider  is 
supported  by  his  saddle,  and  it  is  easy  for  him  to  keep  his  balance 
merely  by  regulating  his  speed.  If  he  is  likely  to  fall  within  the 
ring,  he  increases  his  speed  to  increase  his  centrifugal  force,  which 
throws  his  body  outward,  and  thus  restores  the  equilibrium.  This 
confirms  the  second  law.  The  same  illustration  will  also  confirm 
the  third  law,  for  if  the  ring  be  enlarged  so  as  to  be  very  nearly  a 
straight  line  for  a  short  distance,  the  rider  will  derive  little  or  no 
advantage  from  centrifugal  force  in  maintaining  his  balance,  even  if 
the  velocity  be  greatly  increased. 

260.  Familiar  examples  of  centrifugal  force  are  seen  in 
the  mud  and  water  flying  off  from  the  wheels  of  a  car- 
riage in  rapid  motion.  Large  grindstones  are  frequently 
broken  in  pieces  by  turning  them  too  rapidly.  In  large 
laundries  clothes  are  dried  by  placing  them  in  a  large 
wire  basket,  which  is  then  revolved  many  hundred  times 
a  minute.  Railways,  in  turning  curves,  have  the  outer 

rail  higher  than  the  inner, 
to  counteract  the  centrifugal 
force.  If  a  cup  of  water  be 
balanced  on  the  inner  edge 
of  a  hoop,  the  cup  and  its 
contents  may  be  whirled  over 
the  head  without  spilling  the 
water.  It  has  been  shown 
that  we  may  compute  the  fig- 
ure of  the  earth  by  the  differ- 
ent intensities  of  gravity,  as 
determined  by  the  pendulum, 
and  it  has  been  proved  by  Newton  that  the  spheroidal 
shape  of  the  earth  is  precisely  that  which  a  #lobe  of  plastic 
material  would  take  by  virtue  of  the  centrifugal  force. 


\ 


THE  GYROSCOPE.  133 

An  easy  illustration  of  the  reason  of  the  flattening  of  the 
earth,  is  afforded  by  passing  an  axis  through  two  thin 
hoops  of  tin,  and  twirling  them  around  with  moderate 
velocity.  They  will  take  the  shape  shown  in  Fig.  95. 

261.  If  a  cylinder,  suspended  by  a  string,  which  coin- 
cides with    its   axis,    be    revolved    rapidly   by   twisting   the 
string,  the   centrifugal   force  of  all  the  particles  about  the 
axis  will  be  in  equilibrium,  and  the  direction 

of  the  axis  will  be  unchanged.  If,  however, 
the  string  be  attached  a  little  to  one  side  of 
the  axis,  or,  what  is  the  same  thing,  if  the 
particles  of  the  body  are  not  symmetrically 
disposed  about  the  axis  of  rotation,  the  more 
remote  particles  will  have  a  greater  centri- 
fugal force  than  those  nearer,  and  the  cylinder 
will  throw  itself  into  a  position  such  that  it 
will  revolve  about  an  axis  perpendicular  to 
its  length,  and  passing  through  its  center  of 
gravity,  as  shown  by  the  dotted  lines  of  Fig.  FlG- %- 

96.  Tfie  axis  about  which  a  body  tends  to  revolve  is  the  shortest 
axis  of  its  figure. 

The  same  fact  may  be  shown  by  using,  instead  of  the  cylinder,  a 
cone,  an  oblate  or  prolate  spheroid,  a  ring,  or  a  chain. 

262.  The   gyroscope,   Fig.   97,   is  an   instrument  which 
illustrates  the  composition  of  rotary  motions.     One  form 
of  this  consists  of  a  brass  ring, 

C,  within  which  a  heavy  disk,  T, 
revolves  on  its  own  axis,  inde- 
pendently of  the  ring.  Motion 
is  communicated  to  it,  by  first 
winding  a  cord  about  the  axis, 
and  then  suddenly  pulling  it  off. 
If,  when  the  disk  is  rotating 
speedily,  the  end  of  the  axis  be 
supported  on  a  pivot,  p,  the  axis 
of  the  disk  will  begin  to  revolve  in  a  horizontal  plane 


134  NATURAL   PHILOSOPHY. 

about  the  vertical  support,  pg,  and  in  a  direction  corre- 
sponding with  the  movement  of  the  lower  part  of  the  disk. 

The  forces  which  act  upon  the  instrument  are  the  rotary 
motion  of  the  wheel  about  its  axis,  and  gravity,  which  tends 
to  turn  the  wheel  downward  at  right  angles  to  the  axis. 
The  wheel  moves  in  a  resultant  between  these  two  mo- 
tions. 

If  the  disk  be  set  in  rapid  motion  and  held  in  the  hand 
by  the  ring,  and  we  attempt  to  turn  the  axis  up  or  down, 
it  will  oppose  a  sensible  resistance  to  such  a  change  in  the 
plane  of  its  rotation.  The  momentum  of  the  disk  gives  a 
certain  inertia  by  virtue  of  which  the  instrument  "persists 
in  the  plane  of  ife  rotation." 

If  the  wheel  be  suspended  so  that  gravity  can  not  act  to 
bring  it  downward,  the  axis  will  continue  to  point  in  the 
same  direction  during  the  rotation  of  the  wheel.  This  form 
of  the  gyroscope  is  used  to  demonstrate  the  invariability  of 
the  axis  of  the  earth  during  its  rotation. 

263.  Recapitulation. 

Circular  motion  is  due  to 

Centripetal  force  in  the  direction  of  the  radii. 

Centrifugal  force  in  the  direction  of  the  tangents. 
These  forces  vary, 

(1.)  With  the  weight. 

(2.)  With  the  length  of  the  radii. 

(3.)  With  the  squares  of  the  velocities. 


HYDROSTATICS.  135 


CHAPTER    IV. 

MECHANICS    OF    FLTJIDS. 

264.  Hydrostatics  treats  of  the  equilibrium  and  of  the 
pressure    of  liquids.     Hydrodynamics    treats   of   the    move- 
ments of  liquids.     Hydraulics  considers  the  practical  appli- 
cation of  the  laws  of  Hydrodynamics  to  the  conveying  of 
water  in  pipes. 

265.  All  solids  act  in  masses :  even  the  particles  of  the 
finest  powder  must  each   be  considered  as   a  mass  whose 
figure  is  dependent  on  the  cohesion  of  its  molecules.     On 
the  other  hand,  each  molecule  of  a  fluid  acts  independently 
of  every  other  molecule,  and  will,  therefore,  move  on  the 
application  of  the  slightest  force.     In   practice  it  is  found 
that  the  particles  of  all  liquids  have  some  cohesion,  as  may 
be  seen  by  dropping  them   slowly  from   the  mouth   of  a 
bottle.     The  formation  of  drops  is  an  evidence  of  cohesion, 
and  the  varying  size  of  the  drops  in  different  liquids  is  an 
evidence  that  cohesion  varies  in  liquids  as  well  as  in  solids : 
thus  a  drop  of  alcohol  is  only  two-thirds  the  size  of  a  drop 
of  water,   and   this,   in   turn,   is    smaller   than  a  drop   of 
sirup.     The  greater  the  cohesion  of  its  molecules  the  less 
will   be  the  fluidity  of  the  liquid.     When  the  cohesion  is 
considerable,  as  in  tar,  the  liquid   is  termed  viscous.      Flu- 
idity is  perfect  only  in  aeriform  bodies;  nevertheless,  cohe- 
sion is  not  taken  into  account  in  the  mechanics  of  liquids. 

266.  The  principal  difference  between  liquids  and  gases 
arises    from    the    fact    that    gases    may    be    compressed   to 
almost  any  extent,  while  liquids  may  be  considered  with- 
out material  error  as  non-compressible  fluids.     Nevertheless, 
all   liquids   are    somewhat   reduced    in    volume    when   sub- 
mitted to  pressure.     Under  a  pressure  of  15  pounds  to  the 


136  NATURAL   PHILOSOPHY. 

square  inch,  mercury  suffers  a  compression  of  0.000005 
parts  of  its  original  volume;  water,'  a  compression  of 
0.00005.  It  has  been  found  that,  within  certain  limits, 
water  and  mercury  continue  to  decrease  in  volume  in  the 
same  ratio  under  additional  pressures.  In  every  case,  as 
soon  as  the  pressure  is  removed,  all  fluids  return  to  their 
original  volume. 

Except  for  the  difference  in  compressibility,  liquids  and  gases  are 
governed  by  the  same  laws.  For  this  reason,  the  term  fluid  will  be 
employed  only  when  both  liquid  and  aeriform  bodies  are  meant. 

TRANSMISSION    OF   PRESSURE. 

267.  From  the  constitution  of  liquids  just  determined, 
follows  a  most  important  distinction  between  solids  and 
liquids.  Solids  can  transmit  pressure  only  in  the  direc- 
tion of  the  force  acting  upon  them;  but  liquids  will  trans- 
mit an  impressed  force  in  every  direction — upward,  down- 
ward, sideways — at  the  same  time.  This  fact  may  be 
demonstrated  by  experiment.  Take 
a  vessel  of  any  shape,  in  whose  sides 
are  cylindrical  apertures,  closed  by 
movable  pistons  whose  areas  are  re- 
spectively 1,  2,  3,  4,  5,  and  fill  the 
vessel  with  water.  Suppose  the  pis- 
tons to  play  without  friction  and  the 
water  to  have  no  weight,  then  there 
will  be  no  tendency  to  motion  any- 
where in  the  vessel.  Now  apply  a 

pressure  of  one  pound  upon  the  piston  representing  unity. 
K:wh  molecule  beneath  the  piston  will  be  slijrhtly  pressed, 
and  a  certain  elastic  force  will  be  developed  in  each. 
Karh  one  will  then  react  upward  :ii_r:iin.-t  the  piston,  sidc- 
ways  airain.-t  the  sides  of  the  vessel  or  against  adjoining 
molecules,  and  downward  against  the  molecule.-  beneath. 
The  adjoining  molecules  will  tran>niit  the  pressure  in  a 
like  manner  to  those  of  a  third  series,  and  they  onward, 


PRESSURE.  137 

so  that  every  molecule  in  the  vessel  will  both  receive  and 
transmit  an  equal  pressure.  Therefore,  each  piston  will  be 
thrust  outward  with  a  force  proportional  to  the  number  of 
molecules  beneath  it,  and  as  these  molecules  are  of  the 
same  size,  the  pressure  on  each  piston  will  be  proportional 
to  its  area;  1  will  be  pressed  outward  with  a  force  of  one 
pound,  2,  by  a  force  of  two  pounds,  3,  by  three  pounds, 
etc.  It  will  be  found  necessary  to  apply  the  amount  of 
force  thus  indicated  to  keep  the  pistons  in  place.  Any 
portion  of  the  sides  of  the  vessel,  or  any  solid  immersed 
in  the  fluid,  will  in  like  manner  sustain  pressure  in  pro- 
portion to  the  area  of  its  surface. 

268.  It  is  also  evident  that  the  pressure     .         J^^ 
exerted  on  the  surface  at  any  point  must  be     \*  ^~ 
perpendicular  at  tiiat  point,  for  if  it  is  not, 

it  may  be  resolved  into  two  portions,  one  F|i. 

perpendicular  and    the    other    parallel    to 
the  surface — of  these,  the  former  would  exert  pressure  and 
the  latter  would  produce  motion  in  the  fluid. 

269.  From  similar  experiments,   Blaise  Pascal  deduced 
this  important  law: 

1.  Fluids  submitted  to  pressure  transmit  it  undiminished  in 
every  direction. 

The  following  corollaries  are  a  necessary  consequence: 

2.  The  pressure  sustained  by  any  surf  ace  is  proportional  to 
its  area. 

3.  The  direction  of  the  pressure  at  any  point  is  perpendicular 
to  the  surface  at  that  point. 

No  apparatus  can  perfectly  demonstrate  these  laws,  because  no 
liquid  is  without  weight.  A  rough  demonstration  can  be  had  by 
fitting  open  tubes  to  two  necks  of  a  Woulfe's  bottle  full  of  water, 
and  thrusting  a  cork  into  the  other  neck.  The  height  to  which  the 
water  will  rise  in  the  tubes  will  be  proportionate  to  the  force  of  the 
thrust. 


138 


NATURAL    PHILOSOPHY. 


EFFECT   OF    GRAVITY. 

270.  Fluids  also  exert  pressure  in  consequence  of  their 
weight.     Suppose  the  vessels  A  B  C  D  filled  with  any  liquid 

to  the  level  C  D,  and  con- 
sider each  divided  into  an 
infinite  number  of  strata 
by  horizontal  planes,  in- 
dicated by  the  lines  of 
the  diagram.  Each  stra- 
tum may  then  be  con- 
sidered as  a  cylinder  ex- 
erting a  pressure  on  its  base  equal  to  its  own  weight.  By 
Pascal's  law  the  weight  of  each  stratum  above  will  be 
transmitted  to  each  stratum  below  in  the  ratio  of  their 
areas,  so  that  the  pressure  sustained  by  any  section,  as  A  B, 
G  L,  G  R,  will  be  equal  to  the  weight  of  a  column  of 
liquid  whose  base  equals  the  area  of  the  section  and  whose 
height  equals  its  depth. 

271.  Several  important  conclusions  may  be  deduced  from 
this: 

1.  The  pressure  on  the  bottom  of  a  vessel  is  independent 
of  the  form  of  the  vessel. 

This  may  be  illustrated  by  Haldat's  apparatus,  Fig.  101.  Fill  the 
bent  tube  with  mercury  to  the  level  c,  and  pour  water  in  the  larger 
•  1  till  it  reaches  the  index  rod  o.  The  water  will  press  the 
mercury  as  high  as  the  ring  a.  Now  replace  the  larger  vessel  M 
by  the  smaller  P,  and  fill  with  water  to  the  index  rod,  when  the 
mercury  will  rise  to  the  same  height  as  l.efoiv,  thus  showing  that 
the  pressure  is  independent  of  the  quantity  of  water,  or  of  the  shape 
of  the  vessel. 

2.  The  pressure   is   proportioned   to   the  density  of  the 
liquid. 

In  the  last  experiment,  if  the  depths  of  the  two  liquids  are 
measured,  it  will  !><•  found  that  the  water  column  is  l."».G  times 
longer  than  the  column  of  mercury. 


UPWARD  PRESSURE. 


139 


FIG.  101. 

3.  The  pressure  exerted  by  a  fluid  is  proportional  to  its 
depth. 

Tie  a  piece  of  sheet  rubber  over  one  end  of  a  long  open  tube. 
On  pouring  water  into  the  tube  the  rubber  will  be  distended  in 
proportion  to  the  depth  of  the  water. 

272.  The  upward  pressure  of  liquids  is  easily  shown  by 
reversing  the  last  experiment :  i.  e. 
by  thrusting  the  closed  end  of  the 
empty  tube  into  water,  when  the 
rubber  will  be  driven  into  the  tube 
farther  and  farther  as  the  depth 
increases. 

It  is  generally  demonstrated  by  taking 
an  open  tube  having  disks  of  lead,  or 
leather  closely  fitting  the  lower  end. 
Support  the  disk  by  a  thread  until  the 
tube  is  plunged  in  a  vessel  of  water. 
The  disk  will  then  be  retained  in  its 
place  by  the  upward  pressure.  If  now 
the  tube  be  carefully  filled,  the  disk  will  FIG.  102. 


140 


NA  T  URA  L   PHIL  OS  OPH  T. 


FIG.  103. 


not  fall  off  until  the  sura  of  the  weights  of  the  interior  column  and 
the  disk  exceeds  the  weight  of  the  exterior  column. 

273.  The  lateral  pressure   of   liquids  is   shown  by  the 
velocity   with  which  they  escape  from   orifices  at  different 
depths, 

A  fine  illustration  is  shown  in 
Fig.  103.  This  consists  of  a  tall 
jar  with  a  stop-cock  near  the  base, 
and  made  to  float  on  the  surface  of 
some  liquid.  If  the  jar  he  filled 
with  water,  and  the  stop-cock  be 
closed,  the  lateral  pressures  at  L 
and  I/  will  be  equal.  Hence, 
equilibrium  will  be  preserved  and 
the  jar  will  remain  at  rest ;  but  on 
opening  the  cock,  the  pressure  at  L 
is  removed,  and  the  lateral  pressure 
at  I/  will  be  effective  in  driving  the 

float  in  the  direction  of  the  arrow  and  opposite  to  the  course  of  the 

stream. 

274.  The  pressure  on  the  bottom  of  a  vessel  is  equal  to 
the  weight  of  a  column  of  fluid  having  the  same  base  as 
the  vessel,  and  a  height  equal  to  the  depth  of  the  fluid  in 
the  vessel. 

If  the  fluid  is  water,  since  a  cubic  foot  of  water  weighs  62.42  Ibs, 
the  total  pressure  equals  the  product  of  the  area  of  the  base  in  feet, 
by  the  depth  in  feet,  and  this  by  62.42.  Thus,  suppose  a  cubical 
vessel  two  feet  on  each  side.  The  pressure  on  the  bottom  will  be 
t-qual  to  2  X  2  X  2  X  62.42  =  499.36  ll.s. 

The  pressure  upon  a  body  sunk  to  any  depth  may  be  calculated  in 
the  same  way. 

275.  The    lateral    pressure    may    be    computed    for  the 
whole   side,   or  for  a  piston    in    the  side,   by  the  following 
rule: 

The  lateral  pressure  upon  any  >iiriar<-  is  equal  to  the 
weight  of  a  column  of  the  fluid,  the  area  of  \vho><-  l»a.^- 
equals  the  area  of  tin-  .-urfarr,  and  whose  height  is  the 


FLUID   PRESSURE.  141 

depth  of  the  center  of  gravity  of  the  surface  below  the 
level  of  the  fluid.  The  center  of  gravity  will  be  at  the 
mean  depth  of  the  surface. 

Suppose  a  square  gate,  C,  in  a  canal  lock  lias 
its  upper  edge  9  feet,  and  its  lower  11  feet  from 
the  surface.  The  area  will  be  4  feet,  the  mean 
depth  9  -f- 11  -H  2  =  10  feet:  hence,  the  pressure 
will  be  4  X  10  X  62.42  =  2496.8  tt>s. 

It  i>  important  to  observe  that  this  pressure 
has  nothing  to  do  with  the  length  of  the  vessel 
in  the  direction  A  B,  or  in  other  words  with  the 
amount  of  back-water;  so  that  the  gates  of  a 
canal  lock  sustains  a  pressure  proportioned  only 
to  the  depth  of  water  and  its  own  area. 

276.  Since  the  area  of  any  given  body  remains  constant, 
the  fluid  pressure  which  it  may  be  made  to  sustain,  will 
vary   as    the    depth.     A    body   submerged    in    fresh   water 
sustains  a  pressure  on  each  square  incli  at  the  depth  of  one 
foot    of  62. 42-=-  144  =  0.4335    pounds.     The    compression 
of  water   is   so    slight    that    even    for   oceanic    depths    the 
pressure  on  each  square  inch   may  be  taken  without  great 
error  in   multiples  of  this   factor.     Thus   the   pressure   on 
each  square  inch  at   10  feet  will  equal  4.335  pounds;    at 
100  feet  43.35  pounds;  at  10000  feet  4335  pounds,  or  over 
two  tons. 

Empty  bottles  hermetically  sealed  have  been  sunk  in  the  open  sea 
with  the  uniform  result  that,  at  no  very  great  depths,  either  the  bot- 
tles have  been  crushed,  or  the  corks  have  been  forced  through  their 
in  k-.  So  pearl  divers  find  it  impossible  to  pass  beyond  a  certain 
depth.  When  a  ship  founders  at  sea,  the  enormous  pressure  at  great 
depths  forces  the  water  into  the  pores  of  the  wood,  and  so  increases 
its  weight  that  no  part  ever  comes  again  to  the  surface. 

277.  Pascal  demonstrated  the  same  fact  for  vessels  con- 
taining fluids,  in  1647.     He  fitted  to  the  upper  head  of  a 
strong   cask    a   tube  of  small   bore   about  forty  feet  long. 
The  cask  being  filled  with  water  he  succeeded  in  bursting  it 


142 


NATURAL   PHILOSOPHY. 


by  pouring  a  very  small  quantity  of  water  into  the  tube.  As 
an  ounce  of  water  will  fill  a  tube  j1^  of  an  inch  in  diameter  and 
40  feet  long,  even  that  quantity  would  have 
sufficed — for  a  tube  -£s  of  an  inch  in  diam- 
eter has  an  area  of  only  ^TT  °f  a  square 
inch,  so  that  the  ounce  pressure  would 
multiply  itself  277  times  for  each  square 
inch  on  the  vessel,  which  becomes  17.34 
pounds  for  each  inch.  Either  head  of  an 
eight  gallon  cask  would  have  to  sustain 
about  2500  pounds,  and  the  total  pressure 
on  the  cask  would  have  exceeded  15,000 
pounds.  The  pressure  would  have  been 
the  same  whatever  the  diameter  of  the 
tube,  provided  the  length  was  unchanged : 
thus,  had  the  tube  been  an  inch  in  area, 
the  pressure  must  have  been  0.4335  X  40 
=  17.34  Ibs.  to  the  square  inch. 

Pipes    conveying    water   from    high    reservoirs 
should   be  of  great   strength.     A  four-inch   pipe, 
laid  100  feet  below  the  level  of 
the  reservoir,  sustains  an  inter- 
nal pressure  of  more  than  6000 

pounds  on  each  foot  of  its  length.     When  a  drain 

beeomas  clogged,  the  pressure  of  the  accumulated 

water  is  sometimes  sufficient  to  burst  it. 

278.  As  fluid  pressure  is  transmitted 
undiminished  in  all  directions,  it  will  not 
be  affected  by  bends  in  the  tube.  The 
hydrostatic  belloivs  consists  of  two  boards, 
AB,  united  by  stout  leather,  and  a  small 
tube,  c,  communicating  with  the  interior. 
Water  poured  into  the  tube  will  lift  the 
upper  hoard  with  a  force  proportioned  to 
the  height  of  water  in  the  tube.  Each 
foot  in  height  represents  a  pressure  of  0.4335  pounds  to 
the  square  inch:  then-Ion-,  if  the  upper  board  has  an  area 


FIG. 


KM;,  UN;. 


THE  HYDRAULIC  PRESS. 


143 


of  one  hundred  square  inches,  and  the  height  of  the  tube 
is  three  feet,  the  weight  capable  of  being  supported  on  A 
will  equal  .4335  X  100  X  3  =  130.05  pounds. 

279.  If  A  had  been  made  to  rise  toward  an  immovable  bar  placed 
above  it,  any  substance  between  the  board  and  the  bar  would  have  been 
compressed  with  the  force  of  43,35  pounds  for  every  foot  in  the  height 
of  the  tube.     By  increasing  the  length  of  the  tube,  the  pressure  will 
soon  become  great  enough  to  rupture  the  bellows.     The  same  effect 
may  be  produced,  if,  instead  of  lengthening  the   tube,   a    piston  is 
employed  to  force  water  down  the  tube.     By  Pascal's  law,  a  pressure 
equal  to  that  upon  the  piston  would  be  communicated  to  each  equal 
area  in  the  bellows. 

280.  Bramah's  hydraulic  press  is  constructed  on  this 
principle. 


FIG.  107. 


Within  the  collar  of  the  iron  cylinder,  B,  a  cast  iron  ram,  P,  worka 
water  tight.     The  substance  to  be  pressed  is  placed  between  the  ram, 


144  NATURAL   PHILOSOPHY. 

P,  and  the  immovable  plate,  Q.  Water  is  brought  by  a  force  pump 
into  the  small  cylinder,  A,  and  is  thence  driven  by  the  piston,  r, 
through  the  tube,  K,  into  the  larger  cylinder.  The  advantage  gained 
will  be  in  proportion  to  the  areas  of  the  two  cylinders.  If  the  large 
cylinder  is  one  hundred  times  the  area  of  the  small  cylinder,  one 
pound  applied  at  the  piston  will  produce  a  pressure  of  one  hundred 
pounds  on  the  ram.  The  efficiency  of  the  press  is  further  increased 
by  the  handle,  M,  a  lever  of  the  second  class.  If  the  distance  of 
the  fulcrum  to  the  applied  force  is  ten  times  the  distance  to  the  weight, 
a  power  of  one  hundred  pounds  will  transmit  one  thousand  pounds 
to  the  piston,  and  tend  to  raise  the  ram  by  a  force  of  one  hundred 
thousand  pounds. 

281.  In   this  press  very  little  power  is  lost  by  friction, 
and,  practically,  the  advantage  gained  is  limited  only  by 
the  strength  of  the  materials.     Like  all  other  machines,  it 
is  governed  by  the  law  of  virtual  velocities  (157)  and  works 
very  slowly.     In  the  example  supposed,  one  hundred  parts 
of  water  driven  out  of  the  small  cylinder  would  raise  the  ram 
but  one  part.     The  hydraulic  press  is  used  wherever  great 
power  is  to  be  transmitted  through  small  space,  as  in  extract- 
ing oils  from  seeds  and  crude  fats,  in  pressing  cotton,  hay 
for  shipment,  and   in  various  other  industrial  uses.     Two 
of  these   machines   were   employed    to   raise   the    immense 
tubes   of  the  Britannia  Bridge   to   their   proper  elevation. 
Such  was  the  force  employed   to    drive   the  water  into  the 
cylinder,  that  it  was  sufficient  to  raise  a  jet  twenty  thousand 
feet  high,   or  over  the   peak  of  Chimbora/o.     With   such 
pressures,  the  weight  of  the  water  in  the  smaller  cylinder 
becomes  inconsiderable. 

EQUILIBRIUM    OF    LIQUIDS. 

282.  A    liquid    is    not    at   rest   unless   its   particles   ar<> 
somehow  restrained  by  a  vessel  or  its  equivalent.     When 
the  liquid  is  in   equilibrium,  the  force  of  gravity  tends  to 
bring  each   molecule  as  near  the  earth's  center  as  possible. 
This  condition  i-  att;iinc«l  only  when  the  surface  is  perpen- 
dicular to  the  force  of  gravity. 


EQUILIBRIUM   OF  LIQUIDS. 


145 


283.  As  two  verticals,  near  each  other,  are  sensibly 
parallel,  any  liquid  surface  included  between  them  is  level 

or  horizontal. 

Whatever  be  the  shape  of  the  vessel,  its  surface  will  be  level.  In 
:i  cnminon  teapot,  the  water  in  the  pot  is  always  at  the  same  level  as 
that  in  the  spout.  So,  a  liquid  poured  into  any  system  of  communi- 
cating vessels,  will  rise  to  the  same  level  in  each.  A  common  ex- 


FIG.   108. 

pression  for  this  fact  is  "  Water  always  seeks  its  lowest  level."  On 
this  principle,  water  is  conveyed  from  reservoirs  through  pipes  to 
supply  cities:  the  water  will  rise  in  the  pipes  to  the  exact  level  of 
the  reservoir,  and  would  rise  to  the  same  level  in  fountains,  were  it 
not  for  the  resistance  of  the  air,  and  other  impediments  to  motion. 


FIG.  109. 


284.  Many  natural  phenomena  depend  on  the  same 
principle.  The  crust  of  the  earth  is  made  up  of  various 
materials,  arranged  in  strata,  as  in  the  diagram.  Some  of 

N.  P.  10. 


146  NATURAL   PHILOSOPHY. 

these,  as  clay  or  dense  rock,  can  not  be  penetrated  by 
water;  others,  as  gravel  or  sand-stone,  will  permit  it  to 
trickle  through  them.  Let  the  shaded  portions  of  the  dia- 
gram represent  the  impermeable  strata,  and  the  light  por- 
tions the  porous  strata.  The  rain  falling  upon  the  surface 
at  dcbe,  will  seek  its  lowest  level,  and,  as  it  can  not 
penetrate  the  underlying  rock,  will  accumulate  in  whatever 
natural  basins  it  affords.  Thus, 

1.  Whatever  rain  falls  upon  the  surface  b  will  sink  as  low 
as  possible,  and  finally  come  to  the  surface  as  a  spring,  at  s. 

2.  The   rain   falling   upon  c  and   d  will   find  a  natural 
reservoir  at  waudw',  the  overflow  at  w  passing  to  the  lower 
level  at  w':     A  shaft  sunk  to  either  of  these  points  would 
make  a  well. 

3.  The  rain  falling  upon   e  would  be   confined  between 
two  impervious  strata,  one  of  which  would  prevent  its  pass- 
ing to  lower  levels,  and  the  other  prevent  a  natural  outlet. 
For  this  reason  it  must  descend  to  its  lowest  level  between 
the  strata.     A  tube  sunk  through  the  intervening  strata  to 
the  porous  stratum,  as  at  A,  would  allow  the  water  to  rise 
in  it  to  a  height  proportioned  to  the  amount  of  accumulation 
in  the  reservoir.     Such  wells  are  Artesian,  because  they  have 
been  long  employed  for  obtaining  water  at  Artois,  in  France. 

The  Artesian  well  at  Louisville,  Ky.,  was  sunk  to  the  depth  of 
two  thousand  and  eighty-six  feet,  and  delivers,  every  twenty-four 
hours,  at  a  height  of  one  hundred  and  seventy  feet  above  the  surface, 
over  three  hundred  thousand  gallons  of  water,  at  a  constant  temper- 
ature of  76°.5  F. 

285.  A  spirit  level  is  used  to  determine  horizontal  lines, 
B  a  .  _^         and   operates  on    the 

principle   that    water 
always  seeks  its  level. 

Flli-  ""•  This     consists     of    a 

closed  glass  tube,  slightly  curved,  and  nearly  filled  with  sonic  liquid 
not  easily  fro/en.  The  tnlx-  is  then  so  arranged,  in  a  bra.-s  ca-c,  that 
when  the  apparatus  is  perfectly  horizontal,  the  small  bubble  of  air, 
B,  will  lie  exactly  at  the  highest  point. 


BUOYANCY  OF  LIQUIDS.  147 

286.  As  the  verticals  drawn  at  two  distant  points  incline 
toward  each  other,  large  surfaces  of  liquids  are  curved,  to 
correspond  with  the  general  form  of  the  earth's  surface. 

The  surface  of  a  large  body  of  water  is  easily  proved  to 
be  convex,  by  the  phenomena  presented  by  ships  sailing 
from  the  shore.  The  hull  first  disappears,  then  the  lower 
sails,  and  so  on,  until,  at  last,  the  whole  sinks  below  the 
horizon. 

The  amount  of  curvature  increases  as  the  square  of  the  distance, 
as  shown  by  the  following  table : 

Distance  in  miles       1234          567          89          10 
Curvature  in  feet    .667  2.67  6.   10.67   16.67  24.  32.67   42.67  54.   66.67 

From  this  it  appears  that  if  the  eye  of  the  observer  were  at  the 
water's  edge,  an  object  eight  inches  high  would  be  visible  at  the 
distance  of  a  statute  mile.  At  the  distance  of  ten  miles,  the  height 
of  a  visible  object  would  be  over  sixty-six  feet.  A  mountain,  a  mile 
high,  could  be  seen  at  a  distance  of  almost  ninety  miles. 

287.  As  the  earth  revolves  on  its  axis,  the  surface  of 
the  ocean  at  rest  is  actually  perpendicular  to  the  resultant 
of  gravity  and  the  centrifugal  force. 

Under  'the  influence  of  gravity  alone,  the  surface  of  the  ocean 
"would  be  spherical,  but  in  consequence  of  the  centrifugal  force,  it  is 
spheroidal,  being  elevated  at  the  equator  and  depressed  at  the  poles. 
This  spheroidal  surface  is  the  ti*ue  level  of  the  ocean ;  a  horizontal 
plane  at  any  point  is  the  apparent  levd. 

288.  The  attractive  force  of  the  sun  and  moon  constantly 
disturbs  the  true  level  of  the  ocean ;  the  attractive  force  of 
the  earth  as  constantly  tends  to  bring  the  water  to  a  level; 
hence  the  periodical   oscillations   of  ebb   and   flow  in   the 
tides. 

BUOYANCY    OF    LIQUIDS. 

289.  When  any  solid  is  immersed  in  a  fluid,  every  por- 
tion  of  its  surface  will   undergo  pressure,   proportional  to 
its   depth.     The  horizontal   pressures  on   the  sides   of  the 
cube,   Fig.   Ill,  will  all  be  equal  and  opposite,   and  will 


148 


NATURAL  PHILOSOPHY. 


have  no  tendency  to  move  the  solid  in  any  direction.  The 
upper  face  will  be  pressed  downward 
by  the  column  MABN,  and  the  lower 
face  will  be  pressed  upward  by  the 
column  MCDN.  The  solid  is,  there- 
fore, urged  upward  by  a  force  equal 
to  the  difference  between  these  two 
pressures,  which  is  evidently  equal  to 
the  weight  of  the  column  of  the  fluid 
having  the  same  base  and  the  same 
This  force  is  called  the  buoyant  effort 


Fio.  ill. 


height  as  the  solid, 
of  the  fluid. 

Now,  as  the  force  of  gravity  tends  to  lower  the  body, 
and  as  the  buoyant  effort  tends  to  raise  it,  the  effect  of 
buoyancy  will  be  to  lessen  the  weight  of  the  body.  Conse- 
quently, a  solid  immersed  in  any  fluid  loses  an  amount  of 
weight  equal  to  the  weight  of  an  equal  volume  of  the  fluid. 

290.  This  principle  was  discovered  by  Archimedes  about 
230  B.  C.  It  may  be  verified  by  hanging  to  one  arm  of  a 
balance  a  hollow  cylinder,  A,  having  a 
solid  cylinder  of  copper,  B,  which  exactly 
fits  within  it,  suspended  from  the  scale 
pan  by  a  hook.  Having  first  counter- 
poised the  beam  by  weights  put  in  the 
other  scale  pan,  immerse  the  copper  mass, 
B,  in  water.  The  cylinder  will  then  lose 
a  portion  of  its  weight,  and  the  equilibrium 
will  be  destroyed.  On  filling  the  bucket, 
A,  with  water,  the  equilibrium  will  be 
again  restored;  thus  proving  that  the  loss 
of  weight  occasioned  by  the  immersion  of 
the  solid  in  water,  is  exactly  equal  to  the 
weight  of  an  equal  volume  of  water. 

The  same  truth  is  exemplified  by  the  fact  that  a  ma-s  i,f  -tone  can 
be  more  easily  lifted  at  the  bottom  of  the  sea  than  on  land,  bein# 
lighter  by  the  weight  of  an  equal  bulk  of  water. 


FLOATING   BODIES. 


149 


291.  When  different  solids  are  thrown  into  a  given 
liquid,  (1.)  those  that  are  heavier  than  an  equal  volume  of 
the  liquid  will  sink;  (2.)  those  that  are  of  the  same  weight 
for  equal  volumes  will  remain  at  rest  in  any  position  in  the 
liquid ;  (3.)  the  others  will  float.  When  a  solid  floats  on 
a  liquid,  the  weight  of  the  solid  will  be  exactly  equal  to 
the  buoyant  effort  of  the  liquid  which  it  displaces.  Hence, 
A  floating  body  displaces  its  own  weight  of  the  fluid. 

This  principle  may  be  proved  by  the  apparatus  in  Fig.  113,  which 
represents  a  vase  with  an  L  tube,  to  the  base  of  which  a  stop  cock,  r, 
is   attached.     Pour   in  an    amount  of  any 
liquid,  and  mark  the  level  by  the  ring,  a. 
Now  place  a  floating  body  in  the  liquid — 
it  will  raise  the   level  of  the  liquid.     By 
means  of  the  stop  cock,  r,  draw  out  enough 
liquid  to  reduce  the  level  again  to  a.    The 
weight  of  this  liquid  will  be  found  exactly 
equal  to  that  of  the  floating  body. 

Many  solids  that  sink  in  oil  or  alcohol 
will  float  on  water ;  some  woods  that  sink 
in  fresh  water  will  float  on  salt  water; 
iron  and  copper  will  float  on  mercury,  but 
gold  and  platinum  will  sink  in  it. 


FIG.  us. 


292.  If  liquids  which  do  not  mix  are  poured  into  the 
same  vessel,  the  lighter  will  rise  to  the  surface,  as  oil  does 
upon  water. 

An  interesting  experiment  may  be  made  by  pouring  several 
liquids,  of  different  densities,  into  a  tall  jar;  as 
coal-oil,  or  naphtha ;  alcohol  reddened  by  cochi- 
neal ;  water  saturated  by  carbonate  of  potassa  and 
tinged  with  litmus ;  and  mercury.  These,  shaken 
together,  will  come  to  rest  arranged  in  the  order 
of  their  densities.  The  experiment  may  be  fur- 
ther varied  by  floating  balls  of  cork,  wax,  wood, 

and  glass  on  the  different  surfaces. 

-== 

293.  If  dense  solids  are  fashioned  into  FlG-  114- 
thin-walled  vessels,   so  as   so   displace  a  volume  of  water 
whose  weight  is  greater  than  their  own,  the  solids  will  float; 


150 


NA  T  URA  L    PHIL  0  SO  PHY. 


thus,  iron,  wrought  into  ships,  not  merely  floats,  but,  as 
in  the  Great  Eastern,  has  an  enormous  capacity  for  carry- 
ing its  machinery  and  cargoes. 

294.  The  Cartesian  diver  well  exhibits  the  principles  of 
flotation.     This  toy,  which  is  made  in  various  shapes,  con- 
sists, essentially,  of  a  figure  connected  with  a  hollow  bulb, 

having  a  small  opening  be- 
neath. The  bulb  is  filled 
with  water  and  air  to  such 
an  extent  that,  when  placed 
in  a  vessel  nearly  full  of 
water,  it  just  floats.  The 
mouth  of  the  vessel  is 
tightly  covered  with  sheet 
rubber  or  moist  bladder. 
On  applying  pressure  to 
the  rubber  by  the  fingers, 
several  facts  may  be  noted. 

1.  That  pressure  is  transmitted 
undiminished.     The  air  trans- 
mits the  pressure  to  the  water, 
and  this  compresses  the  air  in 
the  bulb,  and  drives  the  water 
within  it. 

2.  That  the  pressure  is  in  all 
directions;  for  the  result  is  the  same  in  every  position  of  the  vessel. 

3.  That  the  pressure  is  as  the  depth ;  for  less  pressure  is  required 
as  the  figure  sinks. 

4.  Before  the   pressure  is  applied,  the  figure  is   lighter  than   the 
water  and   floats;  on   forcing  water  into  the-  hulb,  it  becomrs  h.  ;i\i.  i 
and  sinks.     By  carefully  regulating  the  pressure,  the  figure  inny  In- 
brought  to  rest  at  any  depth. 

295.  In  like  manner,  fishes  are  enabled  to    float    at    any 
depth    by    expanding    or   contracting    an    air    bladder    with 
which  they  are  provided.     The  weight   of  the  human  body 
is   about   the    same   as   that  of  an   equal    bulk   of   water. 
When  the  lungs  are  well  filled  with  air,  the  body  i.-  lighter, 


FIG.  in. 


CENTER    OF  BUOYANCY.  151 

but,  when  the  air  is  expelled,  the  body  is  heavier  than 
water.  Therefore,  if  a  person  lies  on  his  back  in  water, 
so  as  to  leave  only  his  mouth  and  nostrils  out  of  water,  he 
is  not  likely  to  sink.  Drowned  persons  rise  when  enough 
gases  have  been  generated  through  decomposition  to  render 
the  body  specifically  lighter  than  water. 

The  buoyancy  of  swimmers  is  increased  by  the  use  of 
life  preservers,  which  are  bags  filled  with  air  or  cork.  As 
the  buoyant  effort  of  a  liquid  increases  with  its  density, 
ships  draw  less  water  in  the  ocean  than  in  fresh  water;  so, 
also,  it  is  easier  to  swim  in  salt  water  than  in  fresh.  On 
the  same  principle,  farmers  determine  the  saltness  of  brine 
by  observing  whether  an  egg  or  a  potato  will  readily  float 
in  it. 

296.  As  the  weight   of   a  solid  may  be   considered  as 
emanating  from  its  center  of  gravity;  so  the  upward  press- 
ure of  a  liquid  acting  upon  a  floating  body,  may  be  con- 
sidered as  acting  at  a  single  point,  which  is  called  its  center 
of  buoyancy.     This  point  will   evidently  coincide  with  the 
center  of  gravity  of  the  liquid  displaced,    and   may  be  re- 
garded as  the  center  of  support  of  the  floating  body. 

Thus,  in  the  figure,  G 
represents  the  center  of 
gravity  of  the  solid,  and 
O  the  center  of  buoyancy 
of  the  fluid.  A  floating 

body  will  be  in  equilib- 

.    *  FIG.  115. 

num  only  when  the  cen- 
ter of  gravity  and  the  center  of  buoyancy  are  in  the  same  vertical 
line. 

297.  The  equilibrium  will  be  either  neutral,  unstable,  or 
stable. 

1.  The  equilibrium  is  neutral,  when  the  form  of  the  body 
is  such  that  the  relative  positions  of  the  centers  of  gravity 
and  buoyancy  can  not  be  changed.  This  will  be  the  case 
with  spheres  of  uniform  density. 


152  NATURAL   PHILOSOPHY. 

2.  The  equilibrium  will   be  unstable,  when  the  center  of 
gravity  is  over  the  center  of  buoyancy.     The  least  force 
will  then  overturn  it. 

3.  The  equilibrium  will  be  stable,   when  the  center  of 
gravity  is  under  the  center  of  buoyancy.     If  the  body  is 
disturbed  from  this  position,  it  will  constantly  tend  to  re- 
sume its  original  position. 

298.  The  stability  of  ships  increases  with  the  breadth  of 
the  part  submerged,  and  also  increases  in  proportion  as  the 
center  of  gravity  is  lowered.     For  this  reason,  vessels  must 
either  carry  heavy  cargoes  over  their  keels,  or  make  up  the 
deficiency  by  ballast.     In  small   boats,  the  equilibrium   is 
stable  so  long  as  the  passengers  are  kept  near  the  bottom 
of  the  boat;   but  when  they  rise,  the  center  of  gravity  is 
elevated,  the  equilibrium  is  thereby  rendered  unstable,  and 
any  unguarded  movement  will  overturn  the  boat. 

SPECIFIC    GRAVITY. 

299.  To  determine  the  specific  gravity  of  a  substance, 
it  is  necessary  (1.)  to  select  some  standard  for  comparison; 
(2.)  then  to  find  the  weights  of  equal  volumes  of  the  stand- 
ard and  the  body  under  consideration  ;  and,  finally,  (3.)  to 
divide   the  weight  of  the   body  by  the   weight  of  an  equal 
volume  of  the  standard.     The  quotient  will  be  the  specific 
gravity  of  the  substance. 

300.  The  standard    usually  taken   for  aeriform   bodies  is 
air,  but  it   is   probable   that   hydrogen  will  soon  come  into 
general   use.     The   standard   for   all   liquids   and  solids   is 
distilled  water. 

As  all  bodies  vary  in  size  with  the  changes  of  the  weather, 
all  observations  should  be  reduced  to  the  same  conditions 
of  temperature  and  atmospheric  pressure. 

The  normal  pre.-Hin-  adopted  in  this  country  is  thirty 
inches  of  the  barometer;  in  France  it  is  760  in  m.  —  29.922 
inches.  This  item  may  be  neglected,  except  in  the  case 
of  aeriform  bodies. 


SPECIFIC   GRAVITY.  153 

The  usage  respecting  temperature  is  still  unsettled :  many 
retain  the  old  English  standard,  60°  F.,  although  the  ten- 
dency is  to  adopt  the  French,  which  is  the  freezing  point 
of  water,  32°  F.,  for  all  bodies  except  water,  which  is 
taken  at  39°.2  F.,  its  point  of  greatest  density.  Observa- 
tions at  any  other  temperature  are  easily  reduced  to  the 
normal  by  means  of  tables,  specially  prepared  for  that  pur- 
pose. 

301.  Having  this  standard,  the  formula  for  the  specific 
gravity  of  solids  and  liquids  becomes, 

rj-  n  Weight  of  given  volume  of  substance 

L4/ ' J     Weight  of  equal  volume  of  water       ~~  Spe<  lfic  %™^' 

When  any  two  of  these  are  given,  the  other  can  be 
found.  Therefore : 

(1.)  The  weight  of  any  given  volume  of  a  body  equals 
the  specific  gravity  of  the  body  multiplied  by  the  weight  of 
an  equal  volume  of  water. 

(2.)  The  weight  of  any  body  divided  by  its  specific 
gravity  will  equal  its  loss  of  weight  in  water,  or  equal  the 
weight  of  an  equal  volume  of  water. 

(3.)  As  one  cubic  inch  of  water  weighs  252.456  grains,  the 
volume  of  a  solid  may  be  found  by  dividing  its  loss  of 
weight  in  water  by  252.456  grains.  The  quotient  will  be 
the  volume  of  the  solid  expressed  in  cubic  inches. 

302.  The  specific  gravity  of  solids  is  found  by  the  appli- 
cation of  the  principle  of  Archimedes  (289).  Weigh  the  body 
in  air  (=  W),  then  suspend  it  by  a  hair  and  find  its  weight 
in  water  (=W).     The  difference  in   weight  is  the  weight 
of  an  equal  volume  of  water  (=  W—  W').     Therefore,  the 
specific  gravity  may  be  found  by  dividing  its  weight  in  air 
by  its  loss  of  weight  in  water. 

[48.]     Sp.  gr.  =W-s-  (W— W). 

Thus,  a  mass  of  lead  weighing  a  pound  in  air  weighs  14.6  ounces 
in  water.  Its  specific  gravity  is,  therefore,  16  •*•  (16  —  14.6)  =  11.4. 


154  X.I  T URAL   PHILOSOPHY. 

303.  If  the   body  is   lighter  than  water,    sink   it   by 
attaching  a   heavy  mass,  whose  weight  in   air  and  in  water 
is   known,  and   find   the  weight  of  the  combined  bodies  in 
air   and   in   water.     The  loss   of    the   combined    bodies    is 
evidently  the  weight  of  water  equal  to  their  united  volume. 
If  the  loss  sustained  by  the  heavy  body  alone  is  taken  from 
this,   the  remainder  will   be   the  weight  of  water  equal   to 
the  bulk  of  the  lighter  body.     Therefore,  the  weight  of  the 
lighter  body  in  air  divided  by  this  remainder  will  give  its 
specific  gravity. 

Thus,  attach  a  pound  of  lead  to  two  ounces  of  cork.  The  weight 
in  water  will  be  8.6  ounces.  The  loss  of  both  bodies  is  9.4  ounces, 
but  as  the  previous  example  shows  the  lead  loses  1.4  ounces,  the 
weight  of  a  volume  of  water  equal  to  the  cork  is  8  ounces.  There- 
fore the  specific  gravity  of  the  cork  is  2  -f-  8  =  .25. 

304.  If  the  solid  is  soluble  in  water,  weigh  it  in  some 
other  liquid,  and  allow  for  the  difference  between  its  specific 
gravity  and  that  of  water. 

Thus,  131  grains  of  nitrate  of  baryta  lost  32  grains  when  weighed 
in  absolute  alcohol,  having  a  specific  gravity  of  .8.  Its  specific 
gravity,  as  compared  with  alcohol,  is  131  -=-  32  =  4.1 ;  then  4.1  multi- 
pi  it -d  by  .8,  the  specific  gravity  of  alcohol,  equals  3.28,  the  specific 
gravity  of  the  salt. 

305.  The  specific  gravity  of  liquids  is  found  (1)  by  the 

specific  gravity  bottle.  Counterpoise  a  small  flask 
by  a  weight  in  the  other  arm  of  the  balance,  and 
wreigh  exactly  one  hundred  or  one  thousand  grains 
of  water  into  the  flask.  Mark  the  volume  of  the 
water  by  a  line  cut  in  the  glass.  Now  empty 
out  the  water,  fill  the  flask  as  high  as  the  line 
with  the  liquid  whose  specific  gravity  is  sought, 
and  weigh.  The  weight  of  the  liquid  in  grains 
divided  by  one  hundred  or  one  thousand  is  its 
>|»M-ifir  gravity.  The  figure  represents  an  clf^aiit 
11,-,.  form  of  the  one  hundred  grain  flask. 

Thus  a  loo  grain  flask  contains  79.88  -rains  of  alcohol;  hence,  the 
specific  gravity  of  the  alcohol  is  0.7938. 


HYDROMETERS. 


155 


(2).  By  the  specific  gravity  bulb.  Suspend  any  insoluble 
solid  by  a  hair,  and,  having  determined  its  weight  in  air, 
find  its  loss  of  weight  in  water,  and  also 
in  the  liquid.  The  loss  of  weight  is  equal 
to  the  weight  of  the  fluid  displaced  by  the 
same  volume:  hence,  the  loss  in  the 
liquid  divided  by  the  loss  in  water  equals 
the  specific  gravity  of  the  liquid. 

The  figure  represents  a  glass  specific  gravity 
bulb  containing  mercury.  It  can  easily  be  made 
out  of  a  small  test  tube,  and  loaded  with  shot 
instead  of  mercury. 

Suppose  the  air  weight  of  the  bulb  is  480 
grains;  its  water  weight,  400  grains;  its  weight 
in  alcohol,  416  grains.  The  losses  will  be,  re- 
spectively, 80  and  64  grains ;  then  64  -=-  80  =  .8, 
the  specific  gravity  of  alcohol.  Y\G.  117. 

306.  Either  of  these  meth- 
ods affords  accurate  results, 
but  for  rapid  determination, 
hydrometers  are  used.  These 
instruments  are  of  two  kinds. 
(1.)  Hydrometers  of  constant 
volume.  (2.)  Hydrometers  of 
constant  weight. 

1.  Nicholson's  hydrometer. 
This  instrument,  shown  in 
Fig.  118,  consists  of  a  hol- 
low cylindrical  vessel,  B,  to 
which  is  attached  a  lead 
basket,  C.  The  basket  is 
made  heavy  to  bring  the  ap- 
paratus into  a  condition  of 
stable  equilibrium.  A  wire 
FlG-  118-  at  the  top  of  the  vessel  sup- 

ports a  pan,  A,  and  has  a  fixed  point,  O,  marked  on  it. 
To  use  the  apparatus  for  determining  the  specific  gravity 


156  NATURAL   PHILOSOPHY. 

of  liquids,  it  is  only  necessary  to  determine  the  total  weights 
required  to  bring  the  hydrometer  to  the  point  O,  in  distilled 
water,  and  in  the  given  liquid. 

Thus,  suppose  the  hydrometer  weighs  1000  grains,  and  it  in- 
quires 500  grains  additional  to  sink  it  in  water  and  200  grains  to 
sink  it  in  alcohol.  Then,  the  total  weights  are  1500  and  1200  grains. 
1200  -T-  1500  =  0.80,  the  specific  gravity  of  the  alcohol. 

It  may  also  be  used  for  solids.  As  before,  suppose  that 
500  grains  will  sink  the  hydrometer  in  water  to  the  fixed 
point,  O.  Place  any  solid,  not  too  heavy,  as  a  bullet,  on 
the  pan,  A,  and  add  weights  until  the  hydrometer  sinks  to 
O.  It  is  evident  that  the  weight  of  the  body  and  the  added 
weights  are  together  equal  to  500  grains.  Then,  if  100  were 
added,  the  weight  of  the  body,  in  air,  must  be  400  grains. 
Now  place  the  body  in  the  basket,  C;  of  course,  as  the 
body  is  submerged,  it  will  be  buoyed  up  by  a  weight  equal 
to  the  volume  displaced.  It  will  be  necessary  to  make  good 
the  loss,  by  adding  weights  to  the  pan,  A,  enough  to  bring 
the  hydrometer  to  the  fixed  point  once  more. 

Suppose  50  grains  are  required;  then,  as  this  equals  the  weight 
of  a  volume  of  water  the  size  of  the  solid,  400  -r-  50  =  8,  the  spe- 
cific gravity  required. 

When  the  solid  is  lighter  than  water,  it  is  necessary  to  fasten  the 
solid  to  the  basket,  C,  before  submerging  it. 

307.  A  floating  body  has  a  constant  weight,  but  dis- 
places a  greater  volume  of  light  than  of  heavy  liquids. 
Hence,  if  these  relative  volumes  may  be  found,  the  specific 
irravity  of  any  liquid  may  be  calculated  by  dividing  the 
volume  which  a  floating  body  displaces  in  water,  by  the 
volume  which  it  displaces  in  the  given  liquid.  On  this 
principle  hydrometers  of  constant  weight  are  constructed. 

The  common  form  consists  of  a  irla-s  stem,  near  the  bot- 
tom of  which  are  blown  two  small  bulbs.  Sonic  mercury  or 
shot  i<  placed  in  the  lower  bulb,  to  Bfcrve  as  ballast,  and 
the  point  to  which  the  inMrumcnt  sinks  in  pun-  water  is 
marked  on  the  stem.  It  is  then  graduated  l»y  placing  the 


BE  A  UME'S  H  YDR  O  METER. 


157 


FIG.  119. 


instrument  in  a  liquid  whose  specific  gravity  is  known;  the 
point  to  which  it  sinks  is  marked,  and  the  intermediate 
space  subdivided  into  a  scale 
of  degrees,  according  to  the 
fancy  of  the  maker.  As  a  long 
stem  would  be  inconvenient,  it 
is  customary  to  have  two  hy- 
drometers, one  for  liquids 
lighter  than  water,  in  which 
the  zero  point  is  near  the  bulb, 
and  the  other  for  heavier 
liquids,  with  the  zero  point  at 
the  top  of  the  stem. 

308.  Thus  Beaume's  hydrom- 
eter for  liquids  heavier  than 
water,  sinks  in  pure  water  to 
the  zero  mark  near  the  top  of 

the  stem  ;  in  a  solution  containing  fifteen  parts  of  salt  to 
eighty-five  parts  of  water,  it  sinks  to  the  mark  15.  All 
the  subdivisions  of  the  stem  are  of  the  same  size  as  those 
between  0  and  15.  As  the  specific  gravity  of  the  salt  solu- 
tion is  known  to  be  1.1095,  the  specific  gravity  correspond- 
ing to  any  degree  may  be  determined. 

Let  x  equal  the  volume  of  water  equal  to  the  weight  of  the  instru- 
ment to  the  zero  point;  then  x  — 15  will  be  the  volume  of  an  equal 
weight  of  the  salt  solution.  Therefore,  x-*-(x — 15)  =  1.1095,  from 
which,  x,  the  number  of  equal  parts  displaced  by  water  is  found  to  be 
152.  The  number  of  equal  parts  displaced  by  any  other  liquid  will  be 
152  —  n,  in  which  n  represents  the  degrees  on  the  scale.  Conse- 
quently, the  specific  gravity  corresponding  to  any  degree  on  the 
scale  will  be  found  by  the  formula  152-=-  (152  —  n}  =  specific  gravity. 

For  liquids  lighter  than  water,  Beaume  made  the  zero  point  cor- 
respond to  a  solution  containing  ten  per  centum  of  salt,  and  marked 
the  point  at  which  the  instrument  floated  in  pure  water  as  10°.  By 
a  similar  calculation  to  that  previously  employed,  the  formula  for 
the  hydrometer  for  liquids  lighter  than  water,  is  found  to  be:  specific 
gravity  =  146  -=-  (136  +  n). 

Alcohometers,  lactometers,  etc.,  have  scales  arranged  to 


158  NATURAL   PHILOSOPHY. 

show  the  per  cent,  by  volume  or  by  weight  of  the  liquid  in 
a  given  solution. 

309.  The  specific  gravity  of  a  gas  is  always  found  by 
direct  weighings  of  equal  volumes   of  air  and   of  the   gas. 
For  this  purpose,  a  large   flask    is  weighed   (1.)  when  en- 
tirely empty  ;   (2.)  when  full  of  air,  and  (3.)  when  full  of 
the  gas  in  question.     The  weight  of  the  gas  divided  by  the 
weight  of  the  air,  will  be  the  specific  gravity  required. 

The  accurate  determination  of  the  weights  of  aeriform 
bodies  is  attended  with  many  difficulties,  which  can  not  be 
detailed  here. 

As  gases  have  weight,  the  principle  of  Archimedes  applies 
to  bodies  weighed  in  them,  as  well  as  in  other  fluids. 

310.  The  practical   applications  of  specific  gravity  are 
numerous  and  important.     It  enables  the  manufacturer  to 
know  what  degree  of  concentration  a  solution,  or  an   acid, 
has   reached.     Thus,  a  Beaume's    hydrometer  stands  in   a 
well  manufactured   sirup  at   35°,  and  in  strong   sulphuric 
acid  at  66°.      It  often  enables  the  merchant   to  determine 
the  purity  of  the  articles  offered.     Thus,  the  value  of  ardent 
spirits  is  dependent  on  the  proportion  of  alcohol  they  con- 
tain.    This  is  indicated  at  once  by  the  alcohometer. 

311.  The  famous  problem  offered  Archimedes  was  to  determine 
the  purity  of  King  Hiero's  crown.     Suppose  the  crown  to  have  been 
an  alloy  of  gold  and  silver,  weighing  22  ounces  in  air,  and  losing  1.5 
ounces  in  water. 

The  general  solution  of  this  problem,  as  applied  to  any  alloy,  gold 
nugget,  or  other  mineral,  is  as  follows: 

Let  M  be  the  mass  of  the  body,  and  m  its  specific  gravity. 

Let  H  be  the  mass  of  the  heavier  substance,  and  h  its  specific 
gravity. 

Let  L  be  the  mass  of  the  lighter  substance,  and  I  its  specific 
gravity. 

Then,  M  =  H  -f-  L.  Since  the  volume  of  a  substance  equals  its 
mass  divided  by  its  specific  gravity, 

M          IL 


REG  API  TULA  TION.  1  59 

From  these  two  equations,  it  is  found  that 


- 

h  — 

The  specific  gravity  of  the  mass  can  be  determined  the 
usual  way  ;  the  specific  gravity  of  the  components  may  be 
found  by  tables,  or  ascertained  from  fragments  of  the  body. 
The  proportions  of  the  ingredients  may  then  be  found  by 
the  formulas. 

In  the  case  of  the  crown  as  supposed,  the  gold,  being  the  heavier, 
is  found  by  the  first  formula. 


312.  Recapitulation. 

I.  Liquids  are  both  compressible  and  elastic. 

II.  They  transmit  external  pressure  in  every  direction. 

1.  Undiminished. 

2.  Perpendicular  to  their  surfaces. 

3.  Proportional  to  their  areas. 

III.  They  produce  pressure  by  their  weight,  and  transmit  this  as 
if  it  were  an  external  pressure. 

IV.  A  liquid  always  seeks  its  lowest  level.     The  surface  of  a  liquid 
in  equilibrium  is  horizontal. 

1.  At  any  given  vertical,  an  apparent  level. 

2.  Between  distant  verticals,  a  true  level. 

V.  The  upward  pressure  of  a  liquid  upon  a  solid,  wholly  or  par- 
tially submerged,  is  its  buoyant   effort.     This  is  always  equal  to  the 
weight  of  the  fluid  displaced. 

1.  A  submerged  solid  loses  weight,  equal  to  the  weight  of  the  fluid 
of  the  same  volume. 

2.  A  floating  solid  loses  all  its  weight,  and  displaces  a  volume  of 
fluid  equal  to  this  weight. 

VI.  The  specific  gravity  of  bodies  is  found  by  comparison  with 
water  or  air. 

1.  By  the  relative  weights  of  equal  volumes. 

2.  By  the  relative  volumes  of  equal  weights. 


160 


NATURAL   PHILOSOPHY. 


HYDRODYNAMICS. 

313.  If  a  vessel  be  filled  with  any  liquid,  the  pressure  at 
any  point  will  be  proportioned  to  its  depth  below  the  sur- 
face. 

Hence,  if  apertures,  r,  g,  m,  n,  p,  be  made  in  the  vessel,  the 
liquid  will  flow  out  with  unequal  velocities,  being  less  for  r 
than  for  any  point  below  it,  and  equal  for  any  two  points, 
as  p  and  v,  at  the  same  vertical  depth  below  the  surface. 


FIG.  120. 

But  the  velocity  does  not  increase  in  the  simple  ratio  of  the 
depth.  The  jet  at  v  will  tend  to  rise  to  the  level  at  h,  and 
fall-  short  of  it  only  because  of  friction,  the  resistance  of 
the  air,  and  the  weight  of  the  particles  falling  back.  If, 
then,  the  velocity  at  v  is  >uf}i«-i«-iit  in  carry  the  liquid 
through  the  vertical  distance,  hv,  in  opposition  to  gravity, 
this  velocity  must  be  equal  to  that  which  a  body  would 
acquire  in  falling  through  the  same  space.  If  the  aperture 
were  in  the  bottom  of  the  vessel,  the  velocity  of  the  escap- 
ing liquid  would  he  the  >ame  as  if  it  had  i'allen  freely 
through  the  vertical  depth  of  the  liquid  above  the  orifice. 


MOVEMENTS    OF  LIQUIDS.  161 

As  the  same  fact  is  true  of  any  aperture  in  the  side  of  the 
vessel,  the  laws  of  escaping  liquids  are  comprised  in  the 
following : 

THEOREM  OF  TORRICELLI. — Particles  of  liquids,  flowing 
from  an  aperture,  Jiave  Hie  same  velocity  as  if  they  had  fallen 
freely  in  vacuo  from  a  height  equal  to  the  vertical  distance  of 
the  surface  of  the  liquid  above  tfie  center  of  the  aperture. 

This  distance  is  called,  technically,  the  head  or  charge. 

314.  The  velocity  due   to   a  body  falling  through   any 
given  height  is  expressed  by  the  formula  [28.]  v  =  V  2  gh. 
As  the  factors  2  g  are  constant  for  the  same  place,  the  velocity 
ivith  whidi  a  liquid  escapes  varies  as  tJie  square  root  of  Hie  head. 
If  we  assume  #  =  32.16,  the  actual  velocity  of  the  liquid 
may  be  calculated  by  the  formula  v  =  8.02  I/A. 

Conversely,  [49.]  7i  =  v2H- 64.32:  hence,  if  the  velocity  is 
known,  we  may  calculate  the  head  due  to  the  velocity. 

As  water  and  mercury  would  fall,  in  vacuo,  from  the 
same  height  in  the  same  time,  so  they,  or  other  liquids,  will 
flow  with  the  same  velocity  under  the  same  head  :  there- 
fore, the  velocity  is  independent  of  the  density  of  the  liquid. 

315.  The  course  of  a  stream,  spouting  out  in  any  other 
direction   than   the  vertical,  is  that  of  a  parabola,  and  is 
governed   by  the  law  of  projectiles.     The  range  of  a  hori- 
zontal jet  is  easily  calculated.     For  example:  if  the  jet,    g, 
is  four  feet  below  the  surface,  the  velocity  due  to  the  head, 
h,  is  sixteen   feet  per  second.      If  its  elevation  above  the 
point  where  it  strikes,  6,  is  nine  feet,  it  will  be  three-fourths 
of  a  second  in  falling.     Inasmuch  as  these  two  motions  do 
not  interfere  with  each  other,  the  range  will  be  found  by 
multiplying  the  velocity  by  the  time.     (16  X  J  =  12.) 

The  calculation   may   be  simplified   by  the  use   of  the  following 
formula:    R  — 2V^HE,   in   which   R  represents  the  range,   H   the 
depth  below  the  surface  of  the  liquid,  and  E  the  vertical  distance  of 
the  aperture  above  the  point  upon  which  the  .stream  falls. 
N.  P.  11. 


162  NATURAL   PHILOSOPHY. 

As  H  and  E  are  parts  of  the  same  perpendicular,  the  value  of 
R  will  he  greatest  when  H  =  E.  Therefore,  the  range  will  be 
greatest  when  the  aperture  is  at  the  middle  point.  Further,  since 
the  product  of  H  and  E  determines  the  range,  their  values  may  be 
interchanged  without  altering  the  value  of  K;  therefore,  two  jets  at 
equal  distances  above  and  below  the  center  have  the  same  range. 
These  conditions  are  shown  in  the  figure. 

316.  To  calculate  the  volume  of  liquid  discharged  from- 
an  orifice  in  a  given  time,  multiply  the  area  of  the  orifice 
by  the  velocity  of  the  stream   per  second,  and,  then,  this 
product  by  the  number  of  seconds. 

Thus,  if  the  jet  g  have  an  inch  area,  there  will  issue,  in  one  sec- 
ond, a  prism  of  water  one  inch  in  area  and  sixteen  feet  long,  the 
contents  of  which  is  1  X  (16  X  12)  =  192  cubic  inches.  If  the  given 
time  be  three  minutes  (=180  seconds),  the  discharge  will  be  equal 
to  192  X  180  cubic  inches,  or  twenty  cubic  feet. 

317.  The   velocity   of    discharge   will    not   be   constant 
unless  the  liquid  is  kept  at  the  same  level.     If  a  cylindrical 
vessel  is  allowed  to  empty  itself  through  an  orifice  at  the 
bottom,  the  velocity  will  be  uniformly  retarded  as  the  sur- 
face of  the  liquid  sinks.     When  motion,  uniformly  retarded, 
conies  to  an  end,  the  average  velocity  is   half  the  initial 
velocity  (215)  ;    consequently,   the   quantity  of  liquid  dis- 
charged from  a  vessel  allowed  to  empty  itself,  is  just  half 
the  quantity  that  would  have  been  discharged  in  the  same 
time  if  the  original  head  had  been  maintained. 

Conversely,  the  time  required  to  empty  an  unreplenishcd 
vessel  is  double  the  time  required  to  discharge  the  same 
quantity  of  liquid  if  the  original  head  is  maintained. 

318.  The  results  thus  given  by  theory  are  never  attained 
in  practice.     Only  the  central  part  of   the  jet  attains  the 
theoretical  velocity.     The  outer  particles  converge  with  less 
velocity,   and,   by  their  interference,   retard   the  flow.     By 
suspending  in  water  small    particles  of  amber   or  litmus, 
this  convergence  can  be  exhibited  by  the  movement  of  the 
particles.     In   consequence  of  the  interference  of  the  cur- 


r/-:XA    COX  TRACT  A. 


163 


Fio.  121. 


rents,  the  jet  contracts  on  leaving  the  orifice, 
and  at  a  distance  from  the  orifice  equal  to 
half  its  diameter,  the  section  of  the  stream  is 
only  .64  the  area  of  the  orifice.  The  point  of 
greatest  contraction,  VC,  is  called  the  vena 
contracta. 


If  the  wall  of  the  vessel   is  a  thin  plate,  the  area 
and  head  of  the  vena  contracta  must  be  considered  as 
the  real  orifice  in  calculating  the  volume  of  liquid  discharged. 

If  the  wall  of  the  vessel  has  considerable  thickness,  or  if  a  short 
tube  is  attached  to  the  orifice,  the  rate  of  discharge  is  increased.  A 
cylindrical  tube,  or  adjutage,  whose 
length  is  four  times  its  diameter,  in- 
creases the  flow  to  eighty-four  hun- 
dredths  of  that  required  by  theory. 
The  effect  is  still  greater  (.92)  if  the 
discharge  tube  is  made  conical  both 
ways,  first  contracting  like  the  vena 
contracta  and  then  widening.  On  the 
other  hand,  if  the  discharge  pipe 
projects  within  the  vessel,  the  veloc- 
ity is  impeded. 

319.  The  lateral  pressure  ex- 
erted by  a  liquid  in  motion,  is 
always  less  than  when  at  rest. 
If  water  flows  vertically  through 
a  long  cylindrical  pipe,  it  will  ^ 
exert  no  lateral  pressure. 

Suppose  a  reservoir  of  water  to 
be  connected  by  rubber  tubing  con- 
trolled by  a  clamp,  C,  to  a  pipe  which 
is  connected  with  a  cistern  having  a 
discharge  pipe,  <?,  at  the  bottom,  and 
an  open  pipe,  B,  at  the  top.  The 
water  flowing  through  the  pipe  will 
never  entirely  fill  it,  so  long  as  it  is  in  motion,  but  will  be  surrounded 
by  a  thin  film  of  air.  If,  now,  a  small  open  tube,  t,  be  inserted  near 
the  top  of  the  pipe,  the  adhesion  of  the  water  will  drag  down  the 
particles  of  air,  which,  on  rising  through  the  water  in  the  cistern 


164  NATURAL   PHILOSOPHY. 

will  rush  out  in  a  steady  stream  through  B.  On  this  principle  the 
blowers  of  the  Catalan  forges  are  constructed,  but  even  a  small  appa- 
ratus of  this  sort  will  furnish  sullicient  air  for  most  blow-pipe  pur- 
poses. 

Now,  suppose  the  tube,  t,  to  be  connected  by  rubber  tubing  to  a  glass 
tube  dipping  in  some  colored  fluid.  The  water  falling  through  the 
pipe  will,  as  before,  drag  the  surrounding  particles  of  air  along  with 
it,  and  thereby  tend  to  produce  a  vacuum  in  the  tube,  G.  Conse- 
quently, the  liquid  will  be  forced  up  the  tube  by  the  pressure  of 
the  external  air,  to  a  height  proportioned  to  the  rarefaction  of  the 
air  in  the  pipe.  With  a  long  discharge  pipe,  the  flow  may  be  so 
regulated  by  the  clamp,  0,  as  to  produce  a  very  nearly  perfect  vacuum 
in  the  tube,  t.  If,  then,  a  receiver,  R,  be  attached  to  the  tube,  it  will 
soon  be  exhausted  of  most  of  its  contents.  Hence,  this  apparatus 
may  also  be  used  as  an  air  pump.  Sprengel's  and  Bunsen's  air 
pumps  are  constructed  on  this  principle. 

In  Sprengel's  air  pump,  mercury  is  used,  and  the  length 
of  the  discharge  pipe  is  a  little  more  than  thirty  inches. 
The  clamp  should  be  so  regulated  that  the  mercury  may  fall 
intermittently  in  large  drops.  These  drops  will  form  in 
cylinders  and  act  as  valves,  completely  closing  the  pipe, 
and  driving  all  the  air  before  them  out  of  the  apparatus. 
The  mercury  in  the  cistern  will  prevent  the  return  of  the 
air  up  the  tube.  As  fast  as  the  reservoir  is  emptied  it  is 
replenished  from  the  cistern. 

In  Bunsen's  air  pump,  water  is  used.  To  obtain  the 
best  results,  the  discharge  pipe  should  be  at  least  thirty- 
four  feet  long.  This  form  is  very  convenient  for  laboratory 
use,  since  it  needs  for  its  construction  only  to  have  the  bent 
tube,  t,  inserted  into  the  waste  pipe  of  the  sink,  and  that  a 
stream  of  water,  under  proper  control,  should  enter  this 
pipe  a  little  above  the  mouth  of  the  tube. 

320.  In  horizontal  pipes  the  discharge  is  less  than  that 
due  to  the  head,  owing  to  tin-  adhesion  of  the  liquid  t<>  tin- 
pipe,  and  to  the  cohesion  of  the  particles  of  the  liquid. 
The  re.-iManre  to  the  flow  incn-asrs,  (1.)  with  the  length 
of  the  pipe;  (2.)  with  the  number  of  bends  and  obstruc- 


RIVERS.  165 

tions;   (3.)   as  the  diameter  is  diminished;    and  (4.)  very 
nearly  as  the  square  of  the  velocity  of  the  stream. 

The  rate  of  discharge  diminishes  as  the  resistance  increases,  con- 
sequently, unless  a  large  allowance  is  made  for  the  resistance,  the 
quantity  delivered  will  fall  short  of  the  estimate.  Under  ordinary 
circumstances,  the  diameter  of  the  discharge  pipe  should  be  at  least 
one-half  greater  than  that  required  by  theory. 

321.  The  size  of  rivers  depends  on  the  physical  character 
of  the  countries  drained   by  them.     Their  velocity   is  de- 
pendent  on    (1.)    the   volume    of  water  to  be   discharged; 
(2.)  the  shape  of  the  channel,  and   (3.)    the  slope  of  the 
bed. 

Thus  the  velocity  of  a  river  is  greater  during  freshets 
than  in  dry  seasons,  and  is  greater  in  narrow  and  straight 
channels  than  in  a  broad  or  winding  bed.  By  reason  of 
the  friction  of  the  banks  the  velocity  is  greatest  in  mid 
channels,  a  little  below  the  surface,  and  least  near  the 
banks.  As  the  lateral  pressure  diminishes  with  the  velocity, 
the  more  sluggish  particles  at  the  sides  press  upon  the 
central  portions,  and  thus  heap  them  up,  to  produce  equi- 
librium. This  renders  the  surface  slightly  convex. 

322.  The  smallest  inclination  capable  of  giving  motion 
to  water,  is  nearly  one  inch  to  fifteen  miles.     Three  inches 
per  mile,  in  a  smooth,  straight  channel,  give  a  velocity  of 
three  miles  an  hour ;   three  feet  per  mile  are  sufficient  to 
produce  a  mountain  torrent. 

The  wearing  away  of  the  banks  and  bottom  of  a  river  or  canal 
depends  on  the  velocity  of  the  current.  A  velocity  of  thirty  feet  per 
minute  will  not  distuib  clay  or  sand  ;  one  of  forty,  will  sweep  along 
coarse  sand ;  of  sixty,  fine  gravel ;  of  one  hundred  and  twenty, 
rounded  pebbles;  of  one  hundred  and  eighty,  angular  stones.  For 
this  reason,  rapid  rivers  are  stony,  slow  ones  sandy  or  muddy. 

If  the  velocity  of  rivers  were  not  checked  by  friction,  their  force 
would  be  frightful.  The  Ganges,  at  a  distance  of  eighteen  hundred 
mik-s  from  its  mouth,  is  eight  hundred  feet  above  the  level  of  the 
sea.  The  velocity  due  to  this  fall  is  over  one  hundred  and  fifty  miles 
per  hour,  which  is  more  than  fifty  times  the  velocity  actually  attained. 


166 


NATURAL  PHILOSOPHY. 


WATER    POWER. 

323.  Flowing  water  acts  as  a  moving  power,  (1.)  by  its 
weight,  (2.)  by  the  force  of  the  current,  or  (3.)  by  the 
combined  effect  of  both. 

The  gross  power  of  a  fall  of  water  is  equal  to  the  weight 
of  water  discharged  in  a  unit  of  time  multiplied  by  the  head. 

Let  H  represent  the  head,  Q  the  volume  in  cubic  feet 
discharged  per  second,  and  62.4  Ibs.  the  weight  of  one  cubic 
foot  of  water;  then,  Q.H  (62.4)  =  P,  the  gross  power  in  foot- 
pounds per  second. 

If  the  velocity  of  the  stream  is  given,  since  [49.]  H  — 
v2  -T-  64.32,  the  formula  becomes 


[50.] 


As  the  last  factor  does  not  differ  greatly  from  unity,  we 
may  use  the  following  rule  for  most  purposes. 

Tfie  gross  poiver  of  a  water  fall  in  foot-pounds  per  second,  is 
equal  to  the  volume  of  water  discharged,  in  cubic  feet,  multiplied 
by  Hie  square  of  Hie  velocity,  in  feet. 

There  is  always  a  loss  of  energy,  arising  from  the*  shape-  and  fric- 
tion of  the  weir,  so  that  the  effective  power  is  somewhat  less  than  the 
gross. 

324.  Water  wheels  are 
either  vertical  or  horizontal. 
In  vertical  wheels,  the  effect- 
ive power  of  the  stream  is 
applied  to  buckets  or  boards 
fixed  to  the  circumference  of 
the  wheel.  The  wheel  is  con- 
nected with  the  machinery  to 
IK-  moved.  Tin-re  are  throe 
varieties  of  vertical  wheels: 
(1.)  the  overshot,  (2.)  the 
undershot,  (3.)  the  breast 


In 


Ki...    Ul. 

the   overshot 


wJieel, 


wheel. 

Fig.    124, 


the  stream   falls  into 


WATER    WHEELS. 


167 


buckets  at  the  top  of  the  wheel,  and  acts  principally  by  its 
weight. 
In  the  undershot  wheel,  Fig. 

125,  the  stream  strikes  against 
boards   at  the   bottom  of  the 
wheel,  and  acts  by  the  force 
of  the  current. 

In    the    breast   wheel,    Fig.    = 

126,  the  stream  may  be  made 
to  act  both  by  its  weight  and 
the    force    of    the     current. 

High  breast  wheels  receive  the  stream  in  buckets  above  the 
axis;  low  breast  wheels  receive  the  stream  on  boards  below 
the  axis. 


FIG.  125. 


FIG.  126. 

325.  The    availability   of    any    wheel   depends    on   the 
character  of  the   fall.     Undershot  wheels   are  well   adapted 
to  low  falls  with  large  supplies  of  water.     Overshot  wheels 
are  used  with  falls  not  exceeding  sixty  feet  in  height,  and 
are  efficient  even  with  small  streams.     Breast  wheels  require 
a  larger  supply  of  water,  but  the  fall  is  always  less  than 
their  diameter. 

326.  The  efficiency  of  a  wheel  is  largely  dependent  on  the 
shape  of  the  buckets,  or  floats,  and  the  readiness  with  which 
the  water  may  escape  after  having  been  used.     The  actual 


168  NATURAL  PHILOSOPHY. 

impulse  of  the  stream  is  only  the  excess  of  its  velocity 
above  that  of  the  float  boards :  thus,  if  the  stream  has  a 
velocity  of  eight  feet  in  a  second,  and  the  float  boards  three 
feet,  the  velocity  of  impact  is  five  feet.  For  these,  and 
other  reasons,  the  maximum  effect  of  the  wheel  is  always 
less  than  the  effective  power  of  the  stream.  Overshot  and 
high  breast  wheels  utilize  from  .6  to  .8  of  the  power; 
low  breast  wheels,  from  .45  to  .65,  and  undershot  from 
.25  to  .45. 

It  is  important  to  notice  that  the  head  is  the  same, 
whether  the  water  flows  from  an  orifice  in  a  reservoir,  or 
falls  freely  the  same  distance,  as  has  been  shown  in  (313). 

327.  There  are  two  forms  of  horizontal  wheels;  (1.)  the 
reaction,  (2.)  the  turbine. 

The  reaction  wJieel  may  be  repre- 
sented by  Barker's  mill,  which  acts 
on  the  principle  of  unbalanced 
lateral  pressure  (273.) 

A  vertical  axis,  CD,  which  revolves 
upon  a  pivot,  terminates  in  two  hori- 
zontal pipes,  A  and  15,  whose  extremi- 
ties are  curved  in  opposite  directions. 
As  the  fluid  escapes  from  the  orifice  in 
the  ends  of  these  pipes,  the  arms  are 
driven  around  in  opposite  directions  to 
the  flow,  and  may  be  employed  to  com- 
municate motion  to  machinery. 

328.  There  are  three  classes  of  turbines,  and  many  vari- 
eties of  each  class.      One  of  the  most  cfiicicnt  was  invented 
in   1827,  by  M.    Fourneyron.     Fig.    12<H  shows  a   vertical, 
and  Fig.  129,  a  horizontal  section  of  this  turbine. 

A  column  of  water,  confined  by  a  cylinder,  15,  after  descending  in 
its  vertical  axis,  rushes  out  at  the  bottom,  through  a  ureat  number 
of  guides,  (/,  so  a-  to  -trikt-  the  curved  buckets,  //,  of  the  wheel,  and 
make  it  revolve.  The  buckets  are  so  curved  as  (1.  to  receive  the 
impulse  of  the  water  in  the  direction  of  its  great  e>t  eflicirwy;  and 
then  (2.)  to  permit  its  escape  with  the  !<M>I  IOM  of  motion.  The 


TURBINE. 


169 


wheel  is  connected  beneath  the  cylinder  to  the  shaft,  d,  which  passes 
upward  through  the  center  of  the  cylinder,  and  communicates  its 
motion  to  the  gearing  at  the  upper  end  of  the  shaft.  Turbines  are 


FIG.  12s. 


FIG.  129. 

applicable  to  falls  of  any 
height,  from  nine  inches  up- 
ward, and  will  utilize  from 
.75  to  .90  of  the  power  of  the 
water. 

329.  If  it  were  possi- 
ble for  water  to  flow  in  a 
pipe  entirely  unimpeded, 
so  that  its  velocity  would  ever  be  that  required  by  theory 
(8.021/&),  there  would  be  no  lateral  pressure;  and,  if  the 
pipe  were  pierced,    no  water  would  flow  out.     But  when 
the   velocity  is   diminished  by   friction,   and  other   causes, 
a   portion   of  the  pressure   is   not 
carried  off,  and  becomes  a  burst- 
ing  pressure   on   the   pipe.      This 
pressure    is    unequal    at    different 
portions  of  the  pipe.     At  the  end, 
E,  Fig.  130,  where  the  water  flows 
out,  it  is  almost  nothing,  but  in- 
creases   toward    the    reservoir,    as 
shown  by  the  dotted  line,  being,  at  any  point,  equal  to  the 
difference  between  the  calculated  and  actual  velocity. 

If,  now,  the  current  of  water  be  suddenly  stopped,  much 
of  the  momentum  will  be  changed  to  lateral  pressure,  and 
the  water  will  rise  in  the  open  pipes,  a  b  c,  to  a  height  pro- 
portioned to  the  reaction  of  the  momentum.  This  will  be 


FIG.  130. 


170 


NATURAL  PHILOSOPHY. 


greatest  in  the  tubes  near  the  end,  E.  In  common  house- 
hold water  pipes,  if  the  faucet  is  suddenly  closed,  a  certain 
shock  is  felt  near  it,  and,  if  the  head  is  sufficient,  the  pipe 
will  burst. 

330.  The  hydraulic  ram  is  a  contrivance  by  which  the 
impulse  of  running  water,  when  suddenly  checked,  can  fu- 
made available  for  raising  a  portion  of  itself  to  a  consider- 
able height. 

Let  K,  Fig.  131,  be  a  reservoir,  from  which  the  water  flows  through 
the  pipe,  P.  to  the  orifice,  o.  Let  a  conical  valve,  C,  be  fitted  to  this 
orifice,  of  such  weight  as  to  remain  down,  and  leave  the  orifice  open, 
when  it  is  opposed  only  by  the  steady  pressure  of  the  water  in  the 
pipe  and  reservoir.  However,  the  water,  by  flowing  through  the  ori- 
fice, soon  acquires  momentum  sufficient  to  raise  the  valve,  C,  close 
the  orifice,  and  thereby  communicate  a  shock  to  the  pipe. 


FIG.  131. 

A  second  valve,  V,  which  opens  into  an  air  chamber,  A,  is  made 
to  rise  by  the  impulse  of  the  reaction,  and  allow  the  water  to  enter 
the  air  c-hamU-r,  until  the  pressure  of  the  inclosed  air  overcomes  the 
shock  of  the  water. 

The  valve,  V,  now  closes,  C  opens,  and  permits  the  water  to  flow 
out  at  o,  as  before.  The  aeeimmlated  momentum  a^ain  closes  C  and 
forces  a  second  portion  of  w.-iter  into  the  air  chamber,  ami  thus  the 
action  i-  continued  indefinitely. 

The  confined  ;iir  KX>H  ac.piires  sufficient  elastic  force  to  drive  the 
water  in  the  chamber  through  the  exit  pipe,  K,  in  a  continued  >tiv.mi. 
Much  more  water  escapes  at  o  between  the  pulsations  than  can  be 


PNEUMA  TICS.  171 

raised  in  the  exit  pipe,  E.  The  useful  effect  of  this  machine  is  the 
greatest  when  the  height  to  which  the  water  is  raised  does  not  much 
exceed  the  fall  from  the  reservoir,  but  it  diminishes  as  the  height 
increases.  With  a  low  fall  and  only  a  moderate  supply  of  water,  a 
constant  stream  can  be  raised  by  this  machine  to  a  considerable 
height.  A  fall  of  two  feet  is  competent  to  raise  one-fortieth  of  the 
water  expended,  to  a  height  of  forty  feet. 

331.  Recapitulation. 

Running  water  exerts  power  in  proportion  to  the  product  of  its 
volume  and  the  square  of  its  velocity,  diminished  by  the  impediments 
to  motion. 

It  acts  as  a  motive  power: 

Useful 
Effect. 

f  Undershot.  .25 

{Vertical.       j  Breast.  .60 

( Overshot.  .75 

f  Turbine.  .90 

Horizontal.  {Keact.on  4Q 

II.  By  the  impulse  of  one  part  of  the  stream  on 

another Hydraulic  ram.  .50 

7^ 


THE    MECHANICS    OF   AERIFORM    FLUIDS. 

332.  Aeriform   bodies   are  fluids  which  are  highly  com- 
pressible,  elastic,    transparent,  and    usually   colorless.      In 
an  aeriform  fluid,  the  repulsion  of  its  molecules  so  far  ex- 
ceeds their  attraction  for  each  other,  that  they  tend  to  sep- 
arate and  expand   indefinitely  into  space,  unless  controlled 
by  external  forces,  or  pressures.     The  force  with  which  an 
tu-riform  fluid  tends  to  expand,  is  called  its  elastic  force  or 
tension. 

333.  Aeriform  bodies  are  divided  into  vapors  and  gases. 
1.    Vapors  are  produced  by  the  action  of  heat  upon  solids 

and  liquids,  and  readily  return  to  their  original  state  upon 
cooling.     Steam  is  the  type  of  all  vapors. 


172  NATURAL   PHILOSOPHY. 

2.  Coercible   gases   are    aeriform    under  ordinary  circum- 
stances, but  may  be  condensed  into  liquids,  and  even  solids, 
by  the  aid  of  pressure  and  of  low  temperatures ;  as  chlorine, 
carbonic  acid  (CO2).    There  are  twenty-nine  coercible  gases. 

3.  Oxygen,  nitrogen,  hydrogen,  carbonous  oxide  (CO),  and 
nitric  oxide  (NO2),  have  with  great  difficulty  been  also  con- 
densed to  liquids,  in  1877.     Before  that  date  these  gases  were 
called  permanent,  because  it  was  thought  they  could  not  be 
condensed  by  the  means  at  the  service  of  physicists. 

It  is  reasonable  to  suppose  that  as  all  gases  have  been  condensed  to 
liquids,  so  also  all  solids  that  are  not  decomposed  by  heat,  may  be 
changed,  at  temperatures  sufficiently  high,  to  liquids  and  to  vapors. 
Therefore,  the  distinction  between  gases  and  vapors  is  merely  conven- 
tional, as  they  differ  from  each  other  only  in  their  specific  properties, 
as  density,  odor,  etc. 

334.  PNEUMATICS  treats  of  the  mechanical  properties  of 
aeriform  fluids. 

The  atmosphere,  which  is  mainly  a  mixture  of  nitrogen 
and  oxygen,  will  be  assumed  as  the  type  of  all  bodies  in 
the  aeriform  state.  Whatever  physical  property  is  estab- 
lished regarding  atmospheric  air,  is  to  be  understood  as 
applying  to  all  vapors  and  gases. 

Air  has  been  proved  to  possess  extension  and  impenetra- 
bility, the  essential  properties  of  matter,  and  to  have 
mobility,  inertia,  and  momentum.  Like  all  other  fluids,  it 
transmits  pressure  undiminished,  in  every  direction  ;  but, 
as  its  compressibility  far*  exceeds  liquids  like  water,  the 
effect  of  pressure  is  not  felt  as  instantaneously  at  long  dis- 
tances us  in  the  case  of  liquids. 

335.  Tli.-   air  i<   kept  in  its  place  about  the  earth  by  tin- 
joint  action   of  its   molecular    repulsion  and   the  attraction 
of  gravitation.      Consequently,  the  atmosphere,  at  its  upper 
limit,  nm>t    hav.-  a  definite  surface,  like  the  sea.      At  any 
point  on  the  earth's  >urface  tin-  air  will  exert,  \>\  ivaxMi  of 
gravity,   a    pressure   due  to  a   line    of   molecule-,   extending 
from  the  point  to  the   upper   limit  of  the  atmosphere.      At 


ATMOSPHERIC  PRESSURE.  173 

any  given  elevation  above  the  surface  of  the  sea,  the  effect 
of  gravity  in  producing  upward,  downward,  and  lateral 
pressures,  will  be  the  same  as  in  liquids. 

336.  The  pressure  of  the  atmosphere  was  first  ascertained 
by  the  experiments  of  Torricelli,  in  1643.  He  filled  a  glass 
tube,  nearly  three  feet  long,  with  mercury,  closed  the  open 
end  firmly,  and  then  inverted  the 
tube  in  a  cistern  of  mercury.  On 
removing  his  finger,  the  liquid  de- 
scended in  the  tube,  and  finally  came 
to  rest  at  the  height  of  about  thirty 
inches  above  the  level  of  the  liquid  in 
the  cistern,  thus  leaving  a  vacuum  at 
the  top  of  the  tube. 

Now,  as  the  weight  of  the  mer- 
cury tends  to  make  it  flow  out  of 
the  tube,  the  column  must  be  sus- 
tained by  an  equal  and  opposite 
force.  The  philosophers  of  the  day 
thought  they  explained  the  matter 
by  saying  that  "  Nature  abhors  a 
vacuum ;"  but  Torricelli  reasoned 
that,  in  obedience  to  the  law  of 

equilibrium  of  fluid  pressures,  the  force  that  sustains  the 
mercury  in  the  tube  is  the  pressure  of  the  atmosphere  on 
the  mercury  in  the  cistern. 

Pascal  confirmed  Torricelli's  explanation,  by  causing  the 
experiment  to  be  repeated  on  the  top  of  a  mountain.  He 
thus  reasoned:  "If  the  height  of  the  mercury  is  less  at  the 
top  of  a  hill  than  at  the  bottom,  it  will  follow  that  the 
weight  and  pressure  of  the  air  are  the  sole  cause  of  the  sus- 
1  ><•])>!< >n,  and  not  the  horror  of  a  vacuum,  since  it  is  very 
certain  that  there  is  more  air  to  weigh  on  it  at  the  bottom 
than  at  the  top,  while  we  can  not  say  that  nature  abhors  a 
vacuum  at  the  foot  of  a  mountain  more  than  at  its  summit." 
At  the  top  of  the  Puy  de  Dome  the  column  was  found  to  be 


174 


NATURAL   PHILOSOPHY. 


B 


Fia.  133. 


three  inches  lower  than  at  the  bottom,  which  settled  the 
question. 

337.  The  pressure  of  the  atmosphere  is,  therefore,  equal 
to  the  weight  of  a  column  of  liquid  which  it  will  sustain. 
An  instrument  used  for  measuring  atmospheric  pressure  is 
called  a  Barometer. 

The  simplest  form  of  the  barometer  is 
the  Torricellian  tube,  but  for  convenience 
of  transportation,  other  forms  have  been 
devised.  Fortin's  is  one  of  the  best.  Fi^s. 
133  and  134.  It  consists  of  a  straight  glass 
tube,  about  thirty -three  inches  long,  filled 
with  mercury,  and  dipping  into  a  glass 
cistern  containing  the  same  fluid.  The 
base  of  the  cistern,  mn,  is  made  of 
leather,  and  can  be  raised  or  lowered  by 
means  of  a  screw,  C.  On  using  this  barom- 
eter, the  mercury  in  the  cistern  is  brought 
to  a  level  with  the  point  of  an  ivory  pin, 
a,  by  turning  the  screw,  C,  up  or  down. 
The  scale,  B,  gives  the  exact  height  of 
the  column  above  this  point.  The  tube 
and  cistern  are  protected  from  accident 
by  a  brass  case.  In  traveling,  the  interior  of  the  tube 
and  cistern  are  filled  with  mercury  by  raising  the  screw, 
so  as  to  prevent  the  accidental  introduction  of  air.  A 
thermometer  is  attached  to  the  scale.  As  mercury  ex- 
pands by  heat,  all  barometrical  observations  should  be 
ml  need  to  the  same  temperature,  by  tables  prepared  for 
that  purpose. 

It  is  essential  to  a  first  rate  barometer  (1.) 
that  the  mercury  should  be  pure,  (2.)  that  the 
scale  should  measure  the  exact  distance  between 
the  levels  of  the  mercury  in  the  tube  and  cistern, 
(3.)  that  the  vacuum  at  the  top  of  the  tube  be  perfect. 
With  the  bc>t  precautions,  it  will  contain  a  trace  of  tin- 
vapor  of  mercury.  Air  is  excluded  by  ponrinir  the  mer- 
cury int«>  the  tube,  small  portions  at  a  time,  and  boiling  it 
after  each  successive  addition. 


CJ 

Fro.  134. 


PRESSURE   OF   THE  ATMOSPHERE. 


175 


338.  The  pressure  of  the  atmosphere  may  be  estimated 
in  pounds,   or  by  the  height  of  the  barometer.      At  the 
level  of  the   sea,    the   height  of  the   column  varies   from 
28  to  31  inches,  the  average  being  29.922   inches.      The 
weight  of  a  column  of  mercury  of  this  height,  and  one  inch 
in  area  is  14.7  pounds.     We  say,  therefore,  that  the  press- 
ure of  the  atmosphere  is  nearly  fifteen  pounds  to  each  square 
inch  of  surface. 

No  other  liquid  is  so  serviceable  in  the  construction  of 
barometers  as  mercury.  Barometers  have  been  made,  hav- 
ing their  tubes  filled  with  water  and  with  sulphuric  acid, 
but  they  are  very  expensive  and  unwieldy.  The  pressure 
of  the  atmosphere  will  sustain  a  column  of  water  13.6  times 
longer  than  the  column  of  mercury,  or  thirty-four  feet. 

339.  The  pressure  of  the  atmosphere  may  be  illustrated 
by  many  simple  experiments. 


FIG.  136. 


FIG.  135. 

1.  In  the  pneumatic 
inkstand,    Fig.    135, 
the  downward  press- 
ure   of    the    atmos- 
phere on  the  liquid 
in  the  tube  sustains 
the  ink  in  the  bottle. 

AVhen  the  ink  sinks  down  to  the  level  of  the 
neck,  a  bubble  of  air  passes  in  and  forces  out  a 
portion  of  the  ink  into  the  tube. 

2.  Fill   a    tumbler  with   water,   and,   having 
placed   a   thick   slip  of  paper  over  its  mouth, 
press  the   paper  down   tightly  with   the  hand, 
and  invert  the  glass  cautiously.     The  hand  may 
now  be   removed,  and  the  water  will   be   sup- 
ported  in  the  glass  by  the  upward  pressure  of 
the  atmosphere  on  the  paper,  Fig.  136. 

3.  Take  a  small  open  tube,  or  a  pipette,  Fig.  137,  plunge  it  vertically 


FIG.  137. 


176 


XA  TURA  L    PHIL OSOPH  Y. 


in  water  until  it  is  filled,  then  close  the  upper  end  by  the  finger  and 

raise  the  tube.  The  water  will  not  run  out,  because  the  pressure  of 
the  air  keeps  it  up.  Remove  the  linger,  so  that  the  atmosphere  may 
press  above  and  below,  and  the  water  will  fall  by  its  o\vn  weight. 

4.  Water  will  not  How  out  of  a  small  tap  in  a  tight  ban-el,  because 
of  the  lateral  pressure  of  the  atmosphere.     If  this  be  counteracted  by 
admitting   air   through   an   opening    in    the   top,   the  water  will    run 
freely  by  its  o\vn  weight.    Xo  upper  opening  is  required  in  beer  barrels, 
because  of  the  tension  of  the  gases  contained  in  the  beer. 

5.  A  boy's  sucker  is  made  by  attaching  a  stout  string  to  the  center 
of  a  small  circular  piece  of  thick  leather.     The  leather  us  first  soaked 

in  water,  and  then  pressed  firmly 
against  the  smooth  surface  of  a 
stone,  so  as  to  exclude  all  the  air. 
The  two  surfaces  are  now  held  to- 
gether by  the  force  of  fifteen 
pounds  to  the  square  inch,  Fig.  138. 
On  pulling  the  string,  a  vacuum  is 
formed  under  a  portion  of  the 
leather,  and  the  weight  of  the  at- 
mosphere on  its  upper  side  is 
borne  by  the  hand.  The  weight 
of  the  atmosphere  is  thereby  re- 
moved from  this  portion  of  the  stone,  and,  if  it  is 
not  too  heavy,  the  pressure  of  the  atmosphere  on  its 
under  side  will  raise  it  up. 

340.  The  tension  of  gases  may  be  shown 
by  the  following  experiment.  Bend  the 
closed  end  of  a  barometer  tube,  as  in  Fig. 
139,  and  pour  just  enough  mercury  into 
tin-  tube  to  fill  the  bend,  as  shown  in  the 
figure.  The  air  inclosed  in  the  short  arm  is 
now  in  its  natural  condition,  under  the  press- 
ure of  one  atmosphere.  If  thirty  indies  of 
mercury  be  poured  into  tin-  IOHL:  arm,  the  ,.|(.  I3y 

routined    air    will    lie    under   the    procure  of 
two  atmospheres,  one  of  air  and   one   of   mercury,  and   will 
be  reduced  in  volume  one-half.      If  thirty  inches  more  mer- 
cury be  added,  the  pressure  will  lie  three  at inosphrres,  and  the 


FIG.  138. 


TENSION  OF  GASES.  177 

volume  will  be  reduced  to  one-third.  And  so  on,  for  every 
like  increase  of  pressure,  the  volume  will  be  reduced  to 
one-fourth,  one-fifth,  etc.  Therefore, 

1.  The  volume  of  a  given  weight  of  air  is  inversely  as  tfie 
pressure  to  whicJi  it  is  exposed. 

This  proposition  is  known  as  Mariotte's  law,  and  is  true 
for  all  gases,  within  small  limits  of  error.  As  the  density 
of  a  body  is  inversely  as  its  volume,  and  as  the  pressure  is 
always  sustained  by  the  tension  of  the  air  inclosed, 

2.  Tlie  density  and  tension  of  a  given  weight  of  air  are  directly 
as  the  pressure  to  which  it  is  exposed,  and  inversely  as  its  vol- 
ume. 

341.  To  prove  the  same  law  for  pressures  less  than  one 
atmosphere :    Fill  a  long  jar  with  mercury,  and  fill  a  baro- 
meter tube  to  within  four  inches  of  the  top 

with  mercury.  Then  invert  the  tube  in 
the  jar,  and  sink  it  until  the  level  of  the 
mercury  in  the  jar  and  tube  is  the  same. 
The  confined  air  is  now  under  the  pressure 
of  one  atmosphere.  On  raising  the  tube, 
as  in  Fig.  140,  the  tension  of  the  confined 
air  equals  one  atmosphere  minus  the  weight 
of  the  mercury  in  the  tube.  If  the  column 
of  mercury  raised  is  fifteen  inches,  the  air 
will  have  a  tension  of  one-half  an  atmos- 
phere, and  will  have  doubled  its  volume. 
When  the  column  of  mercury  is  20  inches 
the  tension  of  the  air  will  be  one-third  of  an 
atmosphere  (30  —  20  =  10),  and  its  bulk 
will  be  trebled.  Mariotte's  law,  therefore, 
applies  both  to  condensed  and  rarified  air.  F,,;.  140. 

342.  The  tension  of  aeriform  fluids,  may  be  measured  by 
manometers  or  gauges.    One  of  the  simplest  forms  is  the  closed 
manometer,  Fig.  141,  which  acts  on  the  principle  of  Mariotte's 

tube.     It  consists  of  a  U  tube,  closed  at  one  end,  and  half 
N.  P.  12. 


178 


/'////.  O.s'O/7/V. 


FIG.  141. 


filled  with  mercury.      The  closed    end  contains  dry  air,   at 

the  ordinary  tension. 

When  the  open  end  communicates  freely 
with  the  atmosphere,  the  level  of  the  mer- 
cury is  the  same  in  both  tubes.  If  the 
open  end  is  connected  with  aeriform  fluids 
whose  tension  is  to  be  measured,  as  with 
the  steam  is  in  a  boiler,  the  air  will  occupy 
one-half,  one-third,  one-fourth,  etc.,  of  its 
original  space,  according  as  the  pressure 
increases  to  two,  three,  four,  etc.,  atmos- 
pheres. Or  if  the  pressure  is  less  than  one 

atmosphere,  the  air  will  expand  as  the  pressure  diminishes. 

343.  Bourdon's  gauge,  Fig.  142,  is  one  of  the  most 
useful  manometers  known.  It  consists  of  a  metallic  tube, 
AB,  closed  at  one  end,  B,  and  fixed  at 
the  other,  A.  The  cross  section  of  the 
tube  is  a  flattened  ellipse,  having  its 
greatest  breadth  perpendicular  to  the 
plane  in  which  the  tube  is  curved.  When 
the  pressure  within  the  tube  is  greater 
than  the  pressure  without,  the  tube  be- 
comes less  curved,  or  tends  to  straighten; 
when  the  pressure  without  is  the  greater, 
it  becomes  more  curved.  The  extent  of 
the  motion  depends  on  the  elasticity  of 
flexure  in  the  tube.  The  movements  of  the  closed  end 
of  the  tube  are  communicated  by  the  link,  D,  to  an 
index,  which  moves  along  a  graduated  arc.  The  arc  is 
graduated  by  comparison  with  other  manometers.  The 
tube  and  mechanism  are  contained  in  a  brass  box  with  ji 
glass  cover.  The  sensibility  of  tin-  gau.iro  depends  on 
the  flexibility  of  the  tube.  Some  are  made  to  measure 
pressures  of  less  than  one  atmosphere,  and  some  of  sev- 
eral liiindri'd. 

In  steam  gauges,  the  fixed  end   of  the  tube  cominuui- 


Fio.   142. 


AIR    PUMPS. 


179 


cates  with  the  boiler,  by  the  stop- cock,  C.  A  modification 
of  this  gauge  is  well  known  in  this  country,  under  the  name 
of  Ashcroft's  gauge. 

To  measure  pressures  of  less  than  one  atmosphere,  the 
tube  is  exhausted  of  air,  and  the  fixed  end  hermetically 
sealed.  The  stop-cock  is  then  removed.  This  gauge  then 
becomes  an  aneroid  barometer. 


AIR  PUMPS. 


344,  An  air  pump  is  an  instrument  for  removing  the  air 
from  a  closed  vessel. 

Fig.  143  shows  the  Leslie  air  pump,  and  Fig.  144  the 
same  instrument  in  section.  The  receiver,  R,  is  connected 


FIG.  143. 


with  the  cylinder,  C,  by  a  long  bent  tube,  terminating  in  a 
horizontal  brass  plate.     The  mouth  of  the  receiver  and  the 


180 


NA  TURA  L    PHIL  OSOPII V. 


FIG.  144. 


surface  of  the  brass  plate  are  carefully  ground,  so  as  to 
bring  them  in  contact  at  every  point.  The  edge  of  the  re- 
ceiver is  smeared  with  grease,  so  as  to  render  the  connection 
as  close  as  possible. 

When  the  piston,  P,  is  raised 
from  the  bottom  of  the  cylinder, 
the  external  air  closes  the  upper 
valve  ;  the  air  in  the  receiver 
expands,  opens  the  lower  valve, 
p  and  fills  the  cylinder.  When 
the  piston  is  depressed,  the  lower 
valve  closes,  and  the  air  in  the 
cylinder  is  forced  through  the 
upper  valve  out  into  the  atmos- 
phere. As  the  piston  again 
rises,  the  upper  valve  is  closed, 
the  lower  valve  opens,  and  the  confined  air  expands  into 
the  cylinder.  At  every  ascent  and  descent  of  the  piston,  a 
portion  of  air  is  removed  from  the  receiver,  and  this  pro- 
cess may  be  repeated  until  the  tension  of  the  air  remaining 
is  not  sufficient  to  lift  the  lower  valve.  The  receiver  is 
then  said  to  be  exhausted. 

The  tension  of  the  air  in  the  receiver  is  measured  by  a 
gauge,  which  consists  of  a  bent  tube,  leading  from  the  re- 
ceiver to  a  vessel  of  mercury,  H.  The  external  air  forces 
the  mercury  up  the  gauge,  in  proportion  as  the  tension  of 
the  air  in  the  tube  is  diminished.  If  the  exhaustion  were 
perfect,  the  mercury  would  rise  to  about  thirty  inches. 
The  height  of  the  gau^e  indicates  the  difference  between 
the  pressure  of  the  atmosphere  and  the  tension  of  the  air 
in  the  receiver. 

The  air  pump  is  also  provided  with  a,  stop-cock,  S,  Fig. 
144,  to  close  the  communication  between  the  cylinder  and 
receiver  when  n^uiivd.  The  stopper,  A,  is  u>ed  to  admit 
the  external  air  to  the  receiver.  A  third  valve,  T,  is  usu- 
ally placed  in  the  top  of  the  cylinder  to  prevent  I  he  external 
air  from  pressing  on  the  piston. 


AIR  PUMP  EXPERIMENTS.  181 

345.  The"  air  pump  may  be  used  to  perform  a  great 
variety  of  experiments,  illustrating  the  properties  of  the 
air,  only  a  few  of  which  can  be  here  given. 

1.  Tfie  presence  of  air  in  bodies  may  be  shown  by  placing 
a  jar  of  well-water   under  the  receiver.     On  working  the 
pump,  bubbles  of  air  will  be  disengaged  from  the  water. 
Having  freed  the  water  from  air,  fasten  to  the  bottom  of 
the  jar  bits  of  wrood  or  other  solids,  and  repeat  the  experi- 
ment.     The    formation    of   air    bubbles    will    prove    their 
porosity,  and  the  presence  of  air  in  the  pores. 

Many  bottled  liquors  are  charged  with  condensed  gases. 
When  the  pressure  is  removed  by  drawing  the  cork,  the  thin 
liquids,  like  champagne,  sparkle;  viscid  liquids,  like  ale,  froth. 

2.  ExpangibiUty.     Tie  the  neck  of  a  fresh,  flaccid  bladder 
and  place  it  in  the  receiver.     On  exhausting  the  receiver, 
the  bladder  will   dilate,  because  the   air  within  it  expands. 
On  re-admitting  air  to  the  receiver,  the  air  in  the  bladder 
resumes  its  former  volume. 

A  shriveled  apple,  or  a  bunch  of  shriveled  grapes  will 
become  plump  in  an  exhausted  receiver. 

3.  Pressure  of  tfie  atmosphere.     Take  a  small  open  receiver 
and  close  the  upper  end  tightly  with 

a  piece  of  sheet  rubber.  On  work- 
ing the  pump  the  air  wrill  be  with- 
drawn from  below  the  rubber,  and 
the  external  air  will  press  the  rubber 
downward  so  as  to  fill  the  receiver. 

If  the  rubber  is  replaced  by  a 
piece  of  moistened  bladder,  Fig.  145, 
and  the  bladder  suffered  to  dry,  the 
external  pressure  will  generally  be 
sufficient  to  burst  the  bladder  with  a  FIG  145. 

loud  report.     If  the  bladder  is  very 

stout,  or  the  exhaustion  incomplete,  it  may  be  necessary  to 
weaken  the  strength  of  the  membrane  by  puncturing  it 
with  the  point  of  a  pin. 


182 


NATURAL  PHILOSOPHY. 


The  Magdeburg  hemispheres,  Fig.  146,  consist  of  two  hol- 
low brass  hemispheres,  which  fit  together  air  tight.  One  of 
them  may  be  connected  with  the  air 
pump  by  a  tube  and  stop-cock  arrange- 
ment. On  exhausting  the  air  from  the 
interior,  the  two  hemispheres  will  be  held 
together  with  a  force  of  fifteen  pounds  to 
the  square  inch.  If  their  diameter  is 
three  inches,  the  area  of  the  section  will 
be  seven  inches,  and  the  force  which 
holds  them  together  will  be  over  one 
hundred  pounds.  As  the  restraining 
force  is  the  same  in  every  position  in 
which  they  are  held,  the  pressure  of  the 
atmosphere  is  ifie  same  in  every  direction. 

Fig.  147  represents  a  tall 
receiver,  which  terminates  in 
a  metallic  cap,  furnished  with 
a  stop-cock,  a  screw,  and  an 
interior  jet  pipe.  Exhaust 
the  air  from  the  interior  and 
close  the  stop-cock.  Place 
the  mouth  of  the  tube  under 


FIG.  146. 


water  and  open  the  stop-cock. 
The  pressure  of  the  atmos- 
phere will  drive  the  water 

up  the  pipe, 

forming 

what        is 

known       as 

the     vacuum  FI<;.  \\i. 

fountain. 

Tin'  iri  itjlit   ///'/>•/•   consists    of   a    receiver 
which   is  connected  to  the  air  pump  by  an 
opening    in    the    top.       The    lower   end    is 
closed  by  a  piston   or  by  a  stout  rubber  bag.     When   the 


PROPERTIES  OF  AIR. 


183 


air  is  withdrawn  from  the  receiver,  the  bag  is  forced  upward, 
and  carries  with  it  weights  attached  below.  If  the  receiver 
is  five  inches  in  diameter,  nearly  three  hundred  pounds  will 
be  lifted  by  the  upward  pressure  of  the  atmospJiere,  if  the 
vacuum  is  complete. 

4.  When  a  heavy  weight  is  thus  sustained,  the  elasticity 
of  the  air  may  be  shown,  in  a  striking  manner,  by  forcing 
dowrn   the  load  by  the  hand,  and  then  releasing  it.     The 
weight  will  then  oscillate  up  and  down,  as  if  on  an  elastic 
spring. 

5.  The  weight  of  air  may  be   ascertained,   by   taking  a 
vessel  of  known   capacity  and   finding  the  difference  of  its 
weight  when  filled  with  dry  air,  and  when  exhausted  of  air. 
If  the  capacity  of  the  vessel  is  one  hundred  cubic  inches, 
the  difference  of  its  weight  will  be  thirty-one  grains.     There- 
fore, the  weight  of  one  cubic  inch  of  air  is  0.31  grains. 


By    the    principle    of   Archi- 


6. The  buoyancy  of  air. 
medes  (289),  a  solid  im- 
mersed in  a  fluid  loses  an 
amount  of  weight  equal  to 
the  weight  of  an  equal 
volume  of  the  fluid.  Hence, 
every  substance  weighs  less 
in  air  than  in  vacuo. 


Suspend  to  one  arm  of  a 
balance  a  hollow  globe,  Fig. 
149,  or  a  ball  of  cork,  and 
counterpoise  it  with  a  lead 
weight.  Now  place  the  balance 
under  a  receiver  and  exhaust 
the  air.  The  cork  will  fall, 
and  thus  seem  to  be  heavier  than  the  lead. 

If  a  body  is  lighter  than  an  equal  volume  of  air,  it  will  rise  in  it. 
Smoke  rises  in  a  chimney  because  air  is  rarified  by  heat,  A  soap 
bubble  made  from  hot  water  and  filled  with  warm  air  rises,  because 
it  weighs  less  than  the  air  it  displaces.  If  the  soap  bubble  is  filled 
with  hydrogen,  it  rises  rapidly  until  it  bursts. 


FIG.  149. 


184  NATURAL  PHILOSOPHY. 

Balloons  are  varnished  silk  bags,  filled  with  hydrogen  or 
coal  gas.  The  silk  is  strengthened  by  a  netting  of  small 
ropes,  which  also  serve  to  suspend  a  light  basket.  The 
buoyant  effort  of  the  air  in  raising  a  balloon  is  equal  to  the 
difference  between  the  weight  of  the  gas  used  and  the  air 
displaced  by  it.  A  spherical  balloon,  forty  feet  in  diam- 
eter, will  displace  two  thousand  five  hundred  pounds  of  air, 
but  will  contain  less  than  two  hundred  pounds  of  hydrogen. 
The  lifting  force  of  such  a  quantity  of  gas  is  over  a 
ton.  It  is,  therefore,  capable  of  lifting  the  weight  of  the 
silk,  and  other  parts  of  the  balloon,  the  aeronaut,  and  a 
large  quantity  of  sand  used  for  ballast.  If  the  aeronaut 
wishes  to  descend  from  a  height,  he  allows  some  of  the  gas 
to  escape,  by  opening  a  valve  in  the  balloon.  If  he  wishes 
to  rise  again,  he  throws  out  a  portion  of  his  ballast.  The 
greatest  height  ever  reached  in  a  balloon  is  a  little  over 
seven  miles.  This  was  attained  by  an  English  aeronaut, 
named  Glaisher,  in  1861. 

7.  That  air  is  necessary  to  combustion,  may  be  shown  by 
placing  a  lighted   candle  in   a  receiver.     On  working  the 
pump,  the  candle  will  grow  dimmer,  burn  blue,  and  finally 
go  out.     The  smoke  of  the  candle  will  be  seen  to  descend, 
because  there  is  nothing  to  sustain  it. 

8.  That  air  is  necessary  to  animal  life,  may  be  shown  by 
placing  a  bird  or  a  mouse  in   a  receiver.     On   exhausting 
the  air,  the  animal  will  give  evident  signs  of  distress,  and 
will  soon  die. 

The  relations  of  air  to  sound  and  heat  will  be  considered 
hereafter. 

346.  The  condenser  is  an  instrument  for  forcing  a  large 
amount  of  air  into  a  closed  vessel. 

One  of  the  best  forms  is  shown  in  Fig.  150.  It  con>ists 
of  a  cylinder,  C,  in  which  a  solid  piston  works  air  tight. 
There  are  two  valves  in  the  cylinder,  (1.)  the  lateral  valve, 
(i,  which  opens  from  the  outside,  and  (2.)  the  lower  valve, 
b,  which  opens  from  the  inside.  The  receiver,  R,  may  be 


CONDENSER. 


185 


connected  by  a  screw  to  the  cylinder,  and  may  be  opened 
or  closed  by  means  of  stop-cocks  arranged  as  in  the  figure. 

In  using  this  instrument, 
the  condenser  and  receiver 
are  connected  and  the  pis- 
ton driven  down.  This  ac- 
tion condenses  the  air  in  the 
cylinder  enough  to  close 
the  lateral  valve  and  open 
the  lower.  When  the 
piston  has  reached  its  low- 
est point,  all  the  air  will 
be  forced  out  of  the  cylin- 
der into  the  receiver. 
The  confined  air  will  have 
it*  volume  diminished  and 
its  tension  increased.  If 
the  cylinder  and  receiver 
are  of  the  same  size,  the 
condensed  air  will  have 
a  tension  of  two  atmos- 
pheres. On  raising  the 
piston,  the  tension  of  the 
air  in  the  receiver  will 
close  the  lower  valve,  the 
external  atmosphere  will 
open  the  lateral  valve,  and  again  fill  the  cylinder. 

This  operation  may  be  repeated  until  the  receiver  is  filled 
with  air  of  the  tension  desired.  When  the  receiver  is  thus 
charged,  the  stop-cock,  V,  is  closed,  and  the  cylinder  is 
detached. 

By  bringing  the  lateral  valve  in  communication  with  a 
reservoir  containing  any  gas  whatever,  this  gas  will  be 
Withdrawn  from  the  reservoir  and  forced  into  the  receiver. 
In  this  manner  liquids  placed  in  the  receiver  may  be 
charged  with  gases. 


FIG.  150. 


186 


NATURAL   PHILOSOPHY. 


347.  An  air  gun  consists  of  a  charged  receiver,  properly 
connected  to  a  gun  barrel.     After  fitting  a  bullet  to  the 
bottom    of    the    barrel,    a    trigger 
^      turns  the  stop-cock,    and  the  con- 
densed   air    rushes   out  with    great 
force.     A  boy's  pop-gun  also  illus- 
trates the  tension  of  confined  air. 

A  fountain  can  be  arranged  to  play  by 
condensed  air.  Before  charging  the  re- 
ceiver fill  it  partially  with  water,  and 
connect  to  the  stop-cock  a  tube  reaching 
to  the  bottom  of  the  receiver.  When 
the  air  has  been  condensed  and  the  stop- 
cock is  opened,  the  air  will  force  the 
water  in  a  jet  to  a  height  proportional  to  the  tension. 

The  experiment  may  be  varied  by  making  the  stream  turn  a  hori- 
zontal tube,  arranged  on  the  principle  of  Barker's  mill,  Fig.  151. 


FIG.  151. 


THE   HEIGHT    OF    THE    ATMOSPHERE. 

348.  Mercury  is  about  eleven  thousand  times  denser  than 
air,  at  the  level  of  the  sea.  If  air  were  every-where  of 
this  density,  the  height  of  the  atmosphere  required  to  bal- 
ance the  column  of  mercury  in  the  barometer  would  be 
11,000  X  29.922  inches,  or  27,400  feet.  The  pressure  of  air 
may,  therefore,  be  reckoned  as  equal  to  a  column  5.2  miles 
high,  having  throughout  a  density  equal  to  that  of  air  at 
the  sea-level. 

This  would  be  the  actual  height  of  the  atmosphere  if  air 
were  incompressible.  We  know  that  the  air  extends  to  a 
greater  height,  because  aeronauts  have  actually  ascended  to 
higher  altitudes.  Moreover,  as  the  air  at  any  level  is  com- 
pressed by  the  weight  of  the  column  above  it,  the  air 
must  become  rarer  as  we  ascend  from  the  level  of  the  sea. 
If  a  barometer  were  carried  one  thousand  feet  above  the 
sea-level,  the  column  would  descend  about  an  inch.  The 
air  at  this  level  sustain-  a  pressure  one-thirtieth  less  than 
at  the  sea -level,  and,  in  accordance  with  Mariotte's  law, 


HEIGHT   OF   THE  ATMOSPHERE. 


187 


it  is  proportionally  of  less  density.  Therefore,  we  shall 
have  to  ascend  rather  more  than  one  thousand  feet  to  re- 
duce the  column  another  inch;  and  so  on,  in  increasing 
ratio.  At  the  height  of  3.4  miles,  the  barometer  will  stand 
at  fifteen  inches,  showing  that  one-half  the  atmosphere  is 
below  that  level.  Every  additional  ascent  of  3.4  miles  will 
reduce  the  pressure  one-half,  and  consequently  the  density 
of  the  air.  The  following  table  is  prepared  in  accordance 
with  this  rate  of  decrease : 

^Pressure  of  the  Atmosphere  at  different  levels. 


Height  above 
the  sea 
in  miles. 

0 

3.4 

6.8 
10.2 
13.6 

51 


Height  of  the 
barometer 
in  inches. 

Density  of 
the  air. 
Sea-level  =  1. 

30 

1 

15 
7.5 
3.75 

* 
\ 
\ 

1.87 

& 

.0009 


"3  ^TS  8 


At  the  height  of  13.6  miles  the  air  would  be  rarer 
than  hydrogen.  At  the  height  of  fifty  miles  the 
mercury  would  be  elevated  about  one-thousandth 
of  an  inch,  and  the  air  would  be  less  than  one 
thirty-thousandth  of  its  density  at  the  sea-level. 
At  this  height,  therefore,  the  limit  of  the  atmos- 
phere is  practically  reached. 

349.  The  intense  cold  of  the  upper  limits 
of  the  atmosphere,  tends  to  diminish  the  ex- 
pansion of  the  air,  by  diminishing  the  repulsion 
between  its  molecules,  so  that  it  is  probable 
that  the  height  of  the  atmosphere  does  not 
exceed  forty-five  miles.  This  result  is  con- 
firmed by  the  phenomena  of  refraction  of  the 
heavenly  bodies. 

Fig.  152  is  an  attempt  to  represent  to  the 
eye  the  decreasing  pressure  of  the  atmos- 
phere. 


Pressure  in 

pounds  to 

the  square  inch. 

15 
7.5 
3.75 
1.875 
.9375 


.0004 


Fio.  152. 


188  NATURAL  PHILOSOPHY. 

350.  Heights  are  measured  by  the  barometer,  in  accord- 
ance with  the  facts  thus  established.    Observations  are  taken 
at  two  stations  at  very  nearly  the  same  moment.    The  differ- 
ence between  the  two  barometric  columns  will  represent  the 
difference  in  the  heights  of  the  atmospheric  columns  above 
the  two  stations.     Allowance  must  then  be   made  for  the 
temperature  at  the  time  of  observation,  and  for  the  latitude 
of  each  station.     Formulae  have  been  computed  for  this  pur- 
pose, but  they  do  not  fall  within  the  scope  of  this  book.* 

351.  Fluctuations   of  the   barometer.     The   atmosphere 
may  be  regarded  as  an  aerial  ocean,  in  whose  lower  depths 
we  live.     From  the  extreme  mobility  of  its  particles,  it  is 
never  perfectly  at  rest,  but  moves  in  immense  waves  above 
our  heads.     When   the  crest  of  one  of  these  waves  is  over 
the  barometer,  the  column  rises;   and  then  falls  again,  as 
the  depression  of  the  wave  succeeds.     Except  for  extraor- 
dinary causes,  the  range  in  height  at  the  equator  does  not 
exceed  one-fourth  of  an  inch ;  at  New  York  the  range  is 
about  two   inches,   and  in   Great  Britain   it  exceeds  three 
inches.      The   mean   annual   height  at   any   station    is    the 
same   from   year   to    year.      The    mean    annual    height    is 
greatest   (30.04   inches)    near   the    thirty-sixth    parallel   of 
latitude. 

352.  The  barometer  is  subject  to  slight  variations,  which 


*An  approximation  to  the  vertical  distance  between  the  two  stations 

may  In-  found  by  multiplying  the  dinVrenee  of  tin-  logarithms  between 
the  two  barometric  columns  by  601-~>!t  r,«  t.  This,  inn-eased  by  f^-0  of 
Itself  for  every  degree  thai  the  mean  temperature  of  the  two  .stations  is 
above  32"  F.f  will  give  a  result  not  far  from  the  truth. 

ExAMi'LK.— The    barometric    pressures    at    the    bottom   and    top  of  a 
mountain    u.-iv,   respectively,  ;>1.7ir>  and   "JT.Miti.     The   mean    temperature 
K;  i.-qiiiied,  tin-  dillerenee  in  height. 

Log.  of  the  lower  station,  :;i.7J.~.      l.f>Wll) 

Log.  of  tin-  upper  station,  L'T.sMi  • 1,11., us 

I  inference  of  logarithms  of  tin-  two  stations^  ~ .05632 

60159  X  .05632  =  3388  =  approximate  height.  The  coi  red  ion  for  tempera- 
1 1 .  r«  is  (50°  -  32°  =  18°),  18  X  SSUo  X  3388  =  137  feet ;  3388  {  137  -  £325  feet  =  the 
height  more  nearly. 


WEATHER    RULES.  189 

occur  at  regular  periods,  from  hour  to  hour  and  from  day  to 
day.  The  mean  monthly  height  is  greater  in  winter  than 
in  summer.  The  mean  daily  height  occurs  at  about  twelve 
o'clock,  noon,  and  midnight ;  the  maximum  height  is  reached 
between  eight  and  nine  o'clock ;  the  minimum,  between 
three  and  four  o'clock,  both  morning  and  evening.  These 
hours  are,  therefore,  the  best  for  taking  observations. 

353.  Besides  these  periodic  variations,  the  barometer  it, 
subject  to  accidental  variations  which  increase  with  the  lati- 
tude.    It  has  been  noticed  that  such  accidental  variations 
are    often    coincident    with    the    changes    in    the    weather, 
because    the    column   of  air  is   generally    heavier   in    fail 
weather,  and  lighter  in  foul  weather.     The  absolute  height 
of  the  column  varies  with  the  altitude  of  the  station,  and 
affords,  by  itself,  no  indication  of  the  weather  ;  hence,  the 
weather   marks,    "fair,   rain,   wind,"  on    some    barometers, 
are  absolutely  worthless.     The  variations  in  the  height  of 
the  barometer  indicate  changes  in   the  pressure  of  the  at- 
mosphere, which  may  be  followed  by  changes  in  the  weather. 
The  following  rules  are  generally  reliable. 

Rules  for  predicting  changes  in  the  iveather: 

1.  The  rising  of  the  mercury  indicates  the  approach  of  fair  weather; 
the  falling  of  the  mercury  indicates  the  approach  of  foul  weather. 

2.  A  sudden   and  great  fall,  is  the  sure   forerunner  of  a  violent 
storm. 

3.  When  the  barometer  changes  slowly,  a  long  continuance  of  the 
weather  indicated  may  be  expected. 

4.  A  sudden  change  of  the  barometer  indicates  that  the  change  of 
weather  will  not  be  of  long  duration. 

354.  The  body  of  a   man  of  average  size  has  a  surface 
of  about  two  thousand  square  inches.     He,  therefore,  sus- 
tains, at  the  level  of  the  sea,  a  pressure  of  thirty  thousand 
pounds.     It  conveys  a  wrong  notion  to  speak  of  this  press- 
ure  as  a  load ;    on  the  contrary,  the  buoyant  effort  of  the 
air  lifts   the   man,  and   makes  him  press  the  ground  more 


190  NATURAL   PHILOSOPHY. 

lightly  than  he  would  without  it.  The  atmosphere  acts  on 
all  sides  of  a  body  immersed  in  it,  not  as  a  weight,  but  as 
a  crushing  force.  The  reason  wrhy  we  do  not  feel  this  com- 
pressing force  is  because  the  pressure  is  transmitted 
throughout  the  body  by  the  blood  and  other  fluids  of  the 
body.  Hence,  when  the  atmosphere  tends  to  squeeze  in 
the  sides  of  the  blood-vessels,  it  is  met  by  an  equal  out- 
ward pressure,  caused  by  the  pressure  of  the  atmosphere  on 
the  other  parts  of  the  system. 

\Ve  may  become  sensible  of  this  outward  pressure  by  placing  the 
hand  on  a  small  open  receiver  and  exhausting  the  air  from  beneath 
it.  The  external  air  now  acts  as  a  load,  holding  the  hand  firmly  to 
the  receiver.  The  blood,  in  the  under  surface  of  the  hand,  distends 
the  vessels,  and,  if  the  skin  has  been  punctured  with  a  pin,  the  blood 
is  forced  out.  Cupping  glasses  are  made  to  act  on  the  same  prin- 
ciple. 

355.  On  ascending  to  great  heights,  the  respiration  is 
much  accelerated,   because   of  the  rarefaction  of  the    air. 
If  the  ascent  is  made  rapidly,  as  in  a  balloon,  other  uneasy 
sensations  are  often  felt,  which   are  very  likely  occasioned 
by  the  expansion  of  the  air  inclosed  in  the  body.     If  the 
ascent  were  made  slowly,  this  air  would  have  time  to  ac- 
commodate itself  to  its  new  conditions.     If  it  be  true  that 
the  "skin  cracks  and  bursts,  and  the  blood  issues  from  the 
pores   of  the  body,"  at   high  elevations,   as   is   related  by 
travelers  in    South    America,    the    cause    must   be    sought 
rather  in   the  dryness  of  the   air,  or  the  greater  cold,  than 
in  the  diminished  pressure. 

Men  who  descend  in  diving  bells  to  the  depth  of  thirty- 
four  feet,  endure  the  pressure  of  at  least  two  atmospheres 
without  serious  inconvenience. 

MACHINES   FOR  RAISING   WATER. 

356.  If  we  place  one  end  of  an  open  tube  in  water,  and 
apply  the  mouth  to  the  other  end,  \ve  may  cause  the  liquid 
to   rise  in  the   tube  by  suction.      Correctly  speaking,    the 


LIFTING   PUMP. 


191 


effect  of  the  suction  is  to  withdraw  the  air  in  the  tube;  the 
water  is  then  forced  up  the  tube  by  the  pressure  of  the 
atmosphere  on  the  surface  of  the  water  in  the  vo»ol. 

The  common  suction,  or  lifting  pump,  acts  on  the  same 
principle.  It  consists  of  a  barrel,  B,  similar  to  the  cylinder 
of  the  air  pump,  and,  like  it, 
fitted  with  a  piston,  P,  work- 
ing air  tight,  and  two  valves, 
U  and  e,  both  opening  up- 
ward. From  the  bottom  of 
the  barrel  proceeds  the  suction 
pipe,  C,  which  dips  below  the 
surface  of  the  water  to  be 
raised. 

When  the  piston  is  worked, 
the  air  beneath  it  is  rarefied 
more  and  more  at  each  stroke; 
the  pressure  of  the  atmosphere 
on  the  water  outside  of  the 
pipe,  causes  the  water  to  rise 
in  the  pipe  and  enter  the 
cylinder  through  the  lower 
valve.  Xow,  on  forcing  down 
the  piston,  the  lower  valve,  e, 
is  closed,  the  water  forces  open 
the  piston  valve,  U,  and  rises 
above  it.  When  the  piston  is 
again  raised,  the  upper  valve, 
U,  is  closed,  and  the  water 
above  it  is  lifted  to  the  spout 
of  the  pump.  At  the  same 
time,  the  atmospheric  pressure 
on  the  water  in  the  reservoir, 
causes  more  water  to  rise  into  the  barrel  under  the  piston. 

357.  The  length  of  the   suction  pipe  can  never  exceed 
thirty-four  feet,  because  the  pressure  of  the  atmosphere  is 


192 


NA  TURA L  PHIL OSOm  ) ". 


only  capable  of  supporting  a  column  of  water  thirty-four  feet 
high.  Owing  to  variations  in  atmospheric  pressure,  and 
the  imperfect  mechanism  of  the  pump,  the  limit,  in  practice, 
is  less  than  twenty-eight  feet.  There  is,  however,  no  limit 
to  the  height  through  which  water  may  be  lifted  after  it  has 
once  passed  above  the  piston.  In  deep  wells,  the  working 
barrel,  containing  the  piston  and  both  valves,  is  placed  near 
the  bottom.  A  long,  vertical  discharge  pipe,  through  which 
the  piston  rod  plays,  connects  the  working  barrel  to  the 
surface  of  the  ground.  The  atmospheric  pressure  forces 
the  water  from  the  well  into  the  working  barrel ;  the  force 
applied  to  the  piston  lifts  the  water  from  the  working  bar- 
rel to  the  top  of  the  discharge  pipe. 

358.  In  the  forcing  pump,  the  piston  is  made  solid,  and 

the  upper  valve,  ut  is  placed  in  a  lateral  discharge  pipe,  d, 

connected  with  the  bottom  of  the  barrel. 

The  lower  valve  and  suction  pipe  are  the 
same  as  in  the  lifting  pump.  When  the  piston 
is  raised,  the  water  passes  up  the  suction  pipe 
through  the  lower  valve,  e,  into  the  pump  bar- 
rel. On  depressing  the  piston,  the  lower  valve 
closes,  and  the  water  is  forced  through  the 
upper  valve,  u,  into  the  discharge  pipe.  On 
again  raising  the  piston,  the  upper  valve  closes, 
and  prevents  the  water  in  the  discharge  pipe 
from  returning;  the  l<>\ver  valve  opens  to  admit 
more  water  into  the  barrel.  At  each  depres- 
sion of  the  piston,  more  water  is  driven  into 
the  discharge  pipe,  until  it  is  elevated  to  the 
required  height. 


FIG.  154. 


359.  The  water  will  be  ejected  from  such  a  pump  in 
successive  impulses.  When  it  is  desired  to  make  the  stream 
continuous  an  air  chamber  is  attached,  as  in  Fiir.  155. 
When  the  piston  descends,  it  forces  the  water  through  the 
valve,  u,  into  the  air  chamber,  A  ;  tin-  water  partially  fills  the 
chamber,  and  thus  compresses  the  air.  The  tension  of  the 
compressed  air  increases  as  its  bulk  is  diminished,  and  soon 


THE  SIPHON. 


193 


FIG.  155. 


becomes  sufficient  to  force   the  water  in  the  chamber  out 
through  the  tube,  T,  in  a  constant  stream. 

360.  An  ordinary  fire  engine  consists 
of    two    force    pumps,    worked    by   long 
handles,  called  brakes,  and  having  an  air 
chamber  common   to  both.     The  piston 
of  one  barrel  descends  as  the  other  as- 
cends,   by    which   means,    a    continuous 
stream   of  water   is  forced  into  the  air 
chamber,  and   escapes  through   the   dis- 
charging pipe. 

361.  The  siphon  is  employed  for  trans- 
ferring liquids  from  a  higher  to  a  lower 
level.    It  consists  of  a  bent  tube  writh  two 
unequal  arms,  Fig.   156.     In    using  the 
siphon  the  shorter  arm  is  plunged  in  the 

liquid  to  be  transferred.     To  begin  the  action,  the  air  may 

be  removed  from  the  tube  by  suction  at  the  lower  end.     The 

liquid  will  be  forced  up  the  shorter  arm  by  the 

pressure  of  the  atmosphere;    it   will  then  fill 

the    tube    and    continue    to  flow   through    the 

siphon. 

After  the  suction  is  stopped,  the  liquid  is 
pressed  up  in  the  shorter  arm  by  the  weight 
of  the  atmosphere  on  the  surface,  A  B,  minus 
the  weight  of  the  liquid  column,  MI.  So, 
also,  the  liquid  in  the  longer  arm  is  pressed  upward  by  the 
weight  of  the  atmosphere,  minus  the  weight  of  the  liquid 
column,  M  K.  Hence,  the  liquid  is  urged  in  the  direction, 
C  M  F,  by  a  force  equal  to  the  excess  of  the  weight  of  M  K, 
over  that  of  M  I.  If  M  K  and  M  I  were  equal  there  could 
be  no  flow  in  either  direction.  The  greater  the  difference 
in  the  length  of  the  arms,  the  greater  will  be  the  velocity 
of  the  flow. 


362.     These  facts   may  be   prettily  shown  by  the  siphon 

N.  P.  13. 


194 


NA  T  URA  L  PHIL  OS  OP II Y. 


fountain.  Close  the  mouth  of  a  tall  flask,  R,  with  a 
cork,  and  insert  two  glass  tubes,  as  shown  in  Fig.  157. 
The  shorter  arm  should  be  drawn  out  at  the  upper  end  to 

a  very  fine  bore.  On  exhaust- 
ing the  air  from  the  tube,  the 
ordinary  flow  of  the  siphon 
will  commence.  If,  now,  the 
longer  arm  be  lengthened,  by 
attaching  a  rubber  tube,  the  jet 
may  be  made  to  strike  forcibly 
against  the  top  of  the  flask. 
The  force  of  the  jet  may  be 
shown  to  be  dependent  on  the 
difference  of  length  of  the  two 
arms. 

As  the  greatest  pressure  on  the  sur- 
face, A  B,  Fig.  156,  can  never  exceed 
one  atmosphere,  the  vertical  height, 
MI,  of  the  column  sustained  can  never 
exceed  thirty-four  feet,  if  the  liquid 
is  water,  or  thirty  inches  if  the 
liquid  is  mercury. 
Fio.  157.  Bv  drawing 

the  end  of  the 

long  arm  out  to  a  fine  tube,  and  giving  i 

horizontal    or    upward    direction,    it    may 

employed  to  advantage  in  illustrating  the  flow 

of  liquids  through  orifices. 

The  acid  siphon,  Fig.  158,  has  a  suction 
tube  attached  for  convenience  in  exhau<iiii.u' 
tin-  air,  and,  at  the  same  time,  preventing  the 
entrance  of  corrosive  liquids  into  the  mouth.  FIG.  iss. 


IKICTION    OF   FLUIDS    AGAINST    EACH    OTHER. 

363.  The  atomizing  tube  is  a  contrivance  for  breaking 
up  the  particles  of  a  liquid  into  spray.  A  common  form 
is  shown  in  Fig.  159. 

It  consists  of  two  open  tubes,  so  inclined  to  each  other  that  a  jet 


FRICTION   OF  FLUIDS. 


195 


FIG.  159. 


of  fluid  driven  through  one  shall  issue  over  or  near  the  mouth  of 
the  other.  The  blast  tube,  A,  is  usually  contracted  at  its  mouth,  so 
as  to  increase  the  velocity  of  the  stream.  The  lower  end  of  the  suc- 
tion tube,  B,  is  plunged  in  any  liquid,  as  cologne. 

If  a  stream  of  air  is  driven 
forcibly  through  the  blast  tube, 
it  will,  on  issuing  from  the 
mouth,  drag  the  contiguous  par- 
ticles of  air  along  with  it,  and 
thus  produce  a  rarefaction  be- 
hind it.  As  the  air  is  rarefied 
in  the  suction  tube,  B,  the  at- 
mospheric pressure  on  the  li- 
quid will  force  a  column  up- 
ward in  the  tube,  and,  if  the  tube  be  not  too  long,  the  particles  will 
rise  to  the  top.  At  this  point,  the  jet  of  air  will  drag  the  liquid 
molecules  along  with  it,  and  the  two  streams  will  be  mingled  in 
one  of  excessively  fine  spray. 

The  same  principle  is  sometimes  employed  in  producing  a  draft  in 
chimneys  and  locomotives.  In  locomotives  the  waste  steam  is  driven 
through  a  blast  pipe  in  the  smoke  stack  and  carries  the  smoke  along 
with  it,  and  thus  increases  the  draft  of  the  fire. 

364.  The  pneumatic  paradox  affords  another  illustration 
of  the  same  sort.  It  may  be  made  by  taking  two  small 
circular  disks  of  card  board,  and  fitting  to  one  a  small  tube 
or  goose  quill.  Now,  if  the  other  disk  is  placed  above  the 
tube,  and  a  pin  passed  through  the 
center  to  keep  it  from  sliding,  it 
can  not  be  blown  off  by  any  ordi- 
nary current  of  air  driven  through 
the  tube.  Because,  as  the  stream 
of  air  is  driven  between  the  disks, 
a  rarefaction  will  be  produced  at 
the  center  of  the  upper  disk;  the 

air  above  it  will  crowd  it  toward  the  orifice  and  hold  it  the 
more  firmly  as  the  blast  is  made  stronger.  While  the  cur- 
rent of  air  is  passing,  the  tube  may  be  held  in  any  position. 
The  force  requisite  to  blow  away  the  upper  disk  must  exceed 
the  atmospheric  pressure  holding  it  down. 


Fie;.  ICO. 


196  NATURAL   PHILOSOPHY. 

365.  Recapitulation. 

1.  Aeriform  fluids  are  governed  by  the  same  laws  as  liquids,  ex- 
cept that,  by  reason  of  their  compressibility,  their  volume  is  inversely, 
their  density  and  tension  directly  as  the  pressure  to  which  they  are 
subjected. 

2.  All  gases,  like  air,  may  be  shown  to  possess  the  universal  prop- 
erties of  matter;    but,  except  air,  none  are  necessary  to  the  support 
of  animal  life,  and  few  are  concerned  in  ordinary  combustion. 

3.  The  barometer  measures  the  pressure  of  the  atmosphere,  and 
may  be  used : 

1.  To  calculate  the  altitude  of  a  place. 

2.  To  predict  changes  in  the  weather. 

4.  The  pressure  of  the  atmosphere  is  employed   in   pumps    and 
siphons. 

5.  The  friction  of  fluids  against  each  other  is  employed  in  blast 
pipes. 


CHAPTER   V. 

UNDULATIONS. 

366.  The  kinds  of  motion  thus  far  considered  in  me- 
chanics, are  mainly  those  which  relate  to  masses  of  matter 
taken  collectively.  A  pendulum  vibrates  as  a  concrete 
whole,  without  reference  to  the  atoms  of  which  it  is  com- 
posed. Each  molecule  partakes  of  the  vibration  common 
to  the  entire  mass,  and  is  at  rest  with  regard  to  contiguous 
particles.  We  are  now  to  consider  movements  which  in- 
volve the  entire  mass  of  a  body,  by  reason  of  the  tempo- 
rary displacement  of  its  particles. 

The  atoms  of  all  bodies  are  held  in  a  state  of  equilibrium  by  tin- 
joint  :iction  of  the  molecular  forces  and  gravity.  If  the  molecule-  <>l 
any  body  are  disturbed  by  any  external  force,  not  too  great,  they  will 
tend  to  resume  their  original  positions  by  a  series  of  movements,  to 


FORMATION  OF  UNDULATIONS.  197 

and  fro,  which  gradually  decrease  in  extent  and  finally  cease.  Such 
alternating  motions  are  known  as  vibrations,  oscillations,  waves,  or  undu- 
lations, according  to  the  circumstances  under  which  they  are  pro- 
duced. 

367.  Any  body  may  be  thrown  into  vibrations  of  some 
sort,  but  the  character  of  the  waves  formed  varies  (1.)  with 
the  state  of  the  body,  whether  solid,  liquid,  or  aeriform; 
(2.)  with  its  form  and  specific  properties,  and  (3.)  with  the 
nature  of  the  disturbing  force. 

Formation  of  undulations.  If  an  elastic  cord,  AX,  fixed 
at  one  end,  be  stretched  by  the  hand  grasping  the  other 
end,  and  the  hand  be  jerked  upward,  an  apparent  move- 
ment will  be  transmitted  along 

the   cord,   like   the   waves   upon       A x 

water.  The  first  effect  of  the 
jerk  will  be  to  produce  the  crest, 
A  EN,  which  rises  above  the 
position  of  repose.  This  will  be 
succeeded  by  the  corresponding 
hollow,  N  D  O,  depressed  below 
the  horizontal  plane  to  the  same 
extent.  If  the  cord  be  jerked 
but  once,  the  curve,  A  E  N  D  O, 
will  advance  along  the  cord,  as- 
suming successively  the  positions 
II  and  III  until  it  reaches  the 
end,  X.  It  will  then  return  in  an 
inverted  curve,  IV,  V,  and  VI,  again  to  the  hand. 

The  curve,  A  E  N  D  O,  Fig.  1 62,  is  called  a  wave. 

A  N  O  is  the  length  of  the  wave. 

H  E  is  the  height  of  the  wave. 

D  P  is  the  depth  of  the  wave. 

A  E  N  is  called  the  phase  of  elevation  of  the 
wave. 

X  D  O  is  called  the  phase  of  depression  of  the  wave. 
The  greatest  distance  through  which  any  particle  moves  is  called 
the  amplitude  of  vibration,  or  the  intensity  of  the  wave.     It  equals  the 
sum  of  the  height  and  depth  of  the  wave,     H  E  +  D  P. 


198  NATURAL    PHILOSOPHY. 

368.  Although  the  particles  of  the  cord  appear  to  move 
from  one  end  to  the  other,  it  is  evident  that  this  is  impos- 
sible, but  that  each  particle  has  moved  only  up  and  down, 
successively  passing  through  the  highest  and  lowest  points 
of  the  wave.     A  wave  which   moves  in  a  certain  direction 
by  the  successive   motion  of  material  particles,  is  called  a 
progressive  undulation. 

If  a  pebble  be  dropped  into  a  placid  pool,  a  circular  elevation  will 
be  formed  around  the  depression  caused  by  the  pebble.  The  gravity 
of  the  liquid  particles  tends  to  bring  them  to  their  former  level,  but 
their  inertia  will  carry  them  below  the  horizontal  plane,  and,  at  the 
same  time,  extend  the  impulse  to  surrounding  particles.  In  this 
way,  progressive  undulations  will  be  produced  in  ever  widening 
circles.  Each  undulation  will  consist  of  a  phase  of  elevation  and  of 
depression.  The  motion  of  each  particle,  in  obedience  to  the  original 
impulse,  and  to  the  force  of  gravity,  can  only  be  up  and  down,  as  i,s 
proved  by  the  alternate  rise  and  fall  of  bodies  floating  on  the  surface. 
A  progressive  undulation  is,  therefore,  merely  an  advancing  form,  and 
any  apparent  progression  of  the  particles  of  the  wave  is  merely  an 
optical  illusion. 

The  circular  waves  of  liquids  decrease  in  intensity,  and  finally  be- 
come inappreciable,  because  the  number  of  particles  through  which 
the  impulse  is  diffused  increases  as  the  circles  widen. 

369.  The    surface   waves   of   fluids    are   propagated    by 
gravity.     All  other  waves  are  dependent,    mainly,  on   the 
elastic  force  developed  among  the   particles  of  a  body  by 
the  disturbing  force.     Any  body  through  which  waves  are 
transmitted  is  called  a  medium. 

Undulations  may  be  confined  to  the  body  in  which  they  are  formed, 
or  may  be  formed  in  one  body  and  transmitted  through  several 
others.  Thus,  the  vibrations  of  solids  may  be  transmitted  to  water, 
to  the  atmosphere,  or  to  other  solids. 

370.  The    undulations   of   solids   are   dependent  on   the 
degree   of  their  elasticity  and    the    manner    l.y   which    it  is 
developed.     Solids  of  an  elongated  form.  MS  rods  and  tense 
cords,   are  subject  to   (1.)   transverse,   (2.)    torsional.    and 
(3.)   longitudinal   vibrations,  arrordin--  a<  their  clastic  force 
is  developed  by  flexure,  torsion,  or  traction. 


-  D 


LXDULATIONS   OF  SOLIDS.  199 

If  a  rubber  tube  be  suspended  from  one  end,  and  stretched  by  a  weight 
at  the  other,  and  the  weight  be  pulled  down  and  suddenly  let  go. 
the  cord  will  perform  a  series  of  longitudinal  vibration*, 
causing  the  weight,  A,  to  oscillate  alternately  above  and 
below  its  normal  position.  If  the  weight  be  turned  to 
one  side,  so  as  to  twist  the  cord,  and  let  go,  the  torsion 
of  the  cord  will  cause  the  weight  to  oscillate  back  beyond 
its  original  position,  and  then  return  in  a  series  of  torsional 
vibrations.  If  the  cord  be  stretched  and  made  fast  at  both 
ends,  and  then  plucked  at  the  center,  by  drawing  it  out 
and  letting  it  go,  it  will  oscillate  to  and  fro  in  transverse 
vibration*,  as  shown  by  the  dotted  lines  of  the  figure.  FlG'  163 

In  each  case,  the  elasticity  of  the  cord  tends  to  restore 
it  to  the  normal  position,  the  inertia  of  the  cord  carries  it 
beyond,  and  again  develops  the  elastic  force.  The  greater 
the  disturbing  force,  the  greater  will  be  the  amplitude  of 
the  vibration,  E  D ;  but  as  the  elastic  force  increases  with 
the  amplitude,  the  time  of  vibration  will  be  the  same. 
Thus  the  vibrations  of  an  elastic  body,  like  those  of  the 
pendulum,  are  isochronous,  or  performed  in  equal  times. 
Therefore,  the  vibrations  of  the  same  body  will  be  continued 
in  equal  times,  though  with  decreasing  amplitude,  until  they 
are  brought  to  rest  by  gravity  and  the  resistance  of  the 
air. 

The  strings  of  musical  instruments  vibrate  transversely. 
Such  vibrations  are  called  stationary,  because  all  the  parti- 
cles assume  and  complete  their  vibration  at  the  same  time. 
The  motion  from  E  to  D  is  called  a  simple  vibration ;  the 
motion  from  E  back  to  the  same  point  is  called  a  double  or 
complete  vibration.  Hereafter  the  word  vibration  will  be 
used  to  denote  complete  vibrations,  unless  the  contrary  is 
distinctly  stated. 

371.  Let  the  cord  AB  be  divided  into  any  number  of 
equal  parts,  and  be  fixed  temporarily  at  the  points  of  divis- 
ion, as  N  and  X',  and  let  the  segments  be  set  in  vibration 
in  contrary  directions  at  the  same  time,  as  shown  in  Fig. 
164.  Now,  if  the  points  N  and  N'  are  set  free,  no 


200 


NATURAL   PHILOSOPHY. 


change  will  take  place  in  the  vibrations  of  the  cord.     The 

cord  will  remain  at  rest 
at  the  points  N  and  N', 


y-v  /xv  -I"       an(l    stationary    undula- 

tions   will     be    formed 

FlQ  164  along   the   cord,   whose 

phases  of  elevation  and 

depression  will  be  alternately  above  and  below  the  line  A  B. 
Rings  of  paper  placed  along  the  cord  will  be  thrown  into 
vibration  at  every  other  point  than  N  and  N'.  Points  at 
rest  in  a  vibrating  body  are  called  nodes,  as  N  and  N'. 

372.  Progressive   undulations  may  be   converted    into 

stationary.  Suppose  a  progressive  undulation  to  be  started  along 
the  cord,  AB,  by  a  single  jerk;  and  suppose  the  pulse,  A  ?n,  to  be 
completed  in  half  a  second.  The  advancing  wave,  E  F,  will  reach 
the  end  of  the  cord  in  one  second,  and  will  then  begin  to  return. 
At  this  moment,  let  an  equal  impulse  be  started  at  G.  The  two 
pulses  will  meet  at  the  center  of  the  cord  in  opposite  directions ;  the 


FIG.  165. 

advancing  wave  will  tend  to  move  the  point  m  downward,  the  re- 
flected wave  will  have  an  equal  tendency  to  move  it  upward.  The 
point,  m,  being  thus  urged  by  two  equal  and  oppo>ite  forces  at  the 
same  time,  will  become  a  node.  The  two  halves  of  the  cord  will  then 
vibrate  independently  of  each  other,  in  >tati.mary  undulating.  l',y 
timing  the  pulses,  so  that  each  shall  oeeupy  one-third.  one-fourth,  etc., 
of  tin-  length  of  the  cord,  three,  four,  etc.,  nodes  will  be  formed  along 
the  string.  The  segments  between  the  nodes  vibrate  independently  of 
each  other  a~  stationary  undulations,  two,  three,  or  four  times  faster 
than  the  cord  vibrates  a-  a  whole.  The  theoretical  length  of  a  wave 
is  that  of  two  segments,  including  one  phase  of  elevation  and  one  of 


NODES. 


201 


depression.  The  position  of  the  nodal  points  can  be  ascertained  by 
placing  on  the  cord  light  rings  of  paper;  these  will  be  thrown  off  at 
any  point  other  than  a  node. 

373,  A  cord  which  vibrates  transversely  along  its  whole 
length,  can  be  made  to  vibrate  in  any  number  of  segments, 


FIG.  166. 


by  gently  touching  it  at  one  of  its  nodal  points,  one-half, 
one-third,  one-fourth,  etc.,  of  its  length,  either  at  the  mo- 
ment the  cord  is  set  in  motion,  or  after  it  has  begun  to 
vibrate.  The  touch  quenches  the  vibration  at  the  point, 
and  the  string  divides  into  two,  three,  four,  or  more  seg- 
ments, according  to  the  distance  of  the  point  touched  from 
the  end.  Fig.  166. 

374,  The  vibrations  of  all  elastic  solids  bear  a  general 
resemblance  to  those  of  cords.  Transverse  vibrations  may 
be  excited  in  cords,  rods,  or  thin  plates,  by  percussion,  or 
by  the  friction  of  a  resined  fiddle-bow.  Longitudinal 
vibrations  may  be  produced  in  cords  and  rods  by  rapidly 
rubbing  them  in  the  direction  of  their  length  with  a  bit  of 
cloth  or  leather  covered  with  powdered  resin.  The  trans- 
verse vibrations  of  cords  are  maintained  by  the  tension  em- 
ployed in  stretching  them.  All  other  vibrations  are  main- 
tained by  the  elasticity  of  the  material.  By  so  much  as 
this  molecular  elasticity  differs  from  that  developed  by  ten- 
sion, will  the  rapidity  of  the  vibration  differ  from  the 


202 


NATURAL   PHILOSOPHY. 


transverse  vibrations  of  cords.  The  same  rod  will  vibrate 
longitudinally  much  faster  than  transversely. 

375.  The  nodal  lines  in  plates  may  bo  shown  by  a  plate 
of  glass  or   metal   fastened   in   a  horizontal    vice.      If  the 
plate  be  covered  with  fine  sand  and  set  into  vibration,  the 
sand  will  be  thrown  off 

from  the  parts  in  vibra- 
tion and  will  gather  about 
the  nodal  points.  If  the 
vibrations  of  the  plate  are 
quenched  at  any  point  by 
touching  the  plate,  nodal 
lines  will  be  formed  sym- 
metrically on  the  plate, 
as  shown  by  Fig.  167. 
In  this  way,  an  almost 
infinite  number  of  nodal 
lines  may  be  formed. 

If  a  thin  goblet  or 
finger  glass  be  partially 
filled  with  water,  and  FIG.  w*. 

then  rubbed  on  the  edge 

with  a  wet  finger,  the  glass  will  emit  a  musical  sound, 
and  waves  and  nodal  lines  will  be  formed  on  the  surface  of 
the  water. 

376.  Undulations  in  liquids,     The  circular  waves  formed 
on  tin-  surface  <»f  liquids   may  be  considered  as  made  up  of 


an  infinite  number  of  linear  undulations,  extending  in  rays 
equally    from     tin-    center,     in     the    direction    of    the     radii. 


COMBINATION  OF    WAVES.  203 

Whatever  may  be  proved  in  regard   to  one  ray  applies  to 
every  ray  similarly  situated. 

Wave  motion  may  be  illustrated  by  the  apparatus  in  Fig.  168, 
which  consists  of  a  long,  narrow  canal,  with  glass  sides,  partially 
filled  with  water.  On  tilting  either  end,  a  progressive  undulation  will 
pass  to  the  other  end  and  be  there  reflected.  If  new  waves  be 
formed  at  proper  intervals,  by  fresh  impulses,  the  advancing  and 
receding  waves  may  be  made  to  meet  in  any  part  of  the  canal,  and 
in  any  phase  of  their  undulation. 

377.  Combination  of  waves.  The  resultant  motion  pro- 
duced by  the  meeting  of  two  waves,  in  opposite  directions, 
will  be  equal  to  their  algebraic  sum.  It  is  customary  to 
consider  the  elevated  phase  as  positive,  -f-,  and  the  de- 
pressed phase  negative,  — . 

1.  If  the  crest  of  one  wave  coincides  with  the  crest  of 
the  other,  the  height  of  wave   formed  will   equal  the  sum 
of  the  elevations  of  the  two  waves,  and,  consequently,  its 
depth  will  equal  the  sum  of  their  depressions. 

2.  If  the  crest  of  one  wave  coincides  with  the  hollow  of 
the  other,  the  height  of  the  wave  formed  will  equal  the 
difference  of  the  elevations  of  the  twro  superimposed  waves, 
and  its  depth  will  equal  the  difference  of  the  depths  of  their 
depressions. 

3.  If  the  amplitudes  of  two  waves  meeting  in  different 
phases  are  equal,  both  waves  will  disappear  and  the  surface 
become  horizontal.     This  phenomenon,  which  results  in  the 
mutual  destruction  of  waves,  is   called  the  interference  of 
waves. 

4.  If  the  impulses  be  so  timed  that  the  length  of  the 
wave  is  an  aliquot  part  of  the  canal,  as   J,  J,  J,  the  de- 
scending particles  of  one  wave  will  meet  the  ascending  par- 
ticles of  the  opposite,  nodes  will  be  formed,  and  two,  three, 
or  more  stationary  undidationt  will  be  produced,  as  shown  by 
the  dotted  lines  of  the  figure. 


204  NATURAL  PHILOSOPHY. 

378.  The  undulations  of  the  waters  of  the  globe  are  seen 
in  tides,  waves,  and  currents. 

The  tide  wave  is  an  alternate  ebb  and  flow  of  the  waters  of  the 
ocean.  It  is  due  to  the  difference  in  the  attraction  of  the  moon 
upon  different  portions  of  the  ocean,  modified  by  the  attraction  of 
the  sun.  In  theory,  two  tide  waves  encircle  the  earth,  and  puss 
around  it  in  a  little  less  than  twenty-five  hours.  In  fact,  the  advance 
of  the  tide  is  so  retarded  by  the  shape  and  depth  of  the  oceanic- 
basin,  that  the  tide  wave  which  starts  south  of  Australia  does  not 
reach  London  until  forty-eight  hours  afterward.  The  height  of 
the  tide  wave  in  the  open  sea  does  not  exceed  three  feet;  but  in 
wide-mouthed  bays,  like  the  bay  of  Fundy,  it  sometimes  exceeds 
seventy  feet, 

379.  The  ordinary  sea  waves  are  caused  by  the  unequal 
pressure  of  the  wind  upon  the  surface  of  the  water. 

The  average  waves  in  a  storm  do  not  exceed  ten  feet  in  height. 
Dr.  Scoresby  measured  waves  during  a  violent  storm  on  the  At- 
lantic, that  were  forty-three  feet  from  the  crest  to  the  hollow  of  the 
wave,  which  is  their  height  and  depth  combined.  The  length  of  the 
waves  he  found  to  be  five  hundred  and  fifty-nine  feet,  and  their  rate 
of  travel  to  equal  nearly  fifty  feet  per  second.  The  great  height  of 
the  waves  in  a  storm  is  due  to  the  accumulation  of  wave  upon  wave. 
Three  or  four  waves  may  sometimes  be  seen  on  the  same  billow. 
This  storing  of  force,  by  the  successive  increment  of  many  feeble  im- 
pulses, is  a  striking  peculiarity  of  wave  motion.  It  is  not  likely  that 
the  force  of  the  most  violent  storm  extends  to  a  depth  of  more  than 
two  hundred  feet. 

380.  The  waves  continue  long  after  the  wind  dies  away, 
producing  what  is  known  as  a  dead  swell.     These  waters 
in   the   open    sea   have    no   onward    motion   whatever,    but 
while   the  storm   is    raging,    the   wind,    striking    the    water 
more  or  less   obliquely,  has  a  tendency  to  drag  the  surface 
particles   along  with   it,  in   the  same  manner  that    it  drives 
floating  logs  and  ships. 


Sir  .John  II.T^ehel  thinks  that  constant  winds,  like  the  trades, 
are  enmpHriit  In  aeenmnlate,  )>y  their  strady  aetion,  enough  of  this 
sort  of  motion  to  produce  the  oceanic  ••urn-nts.  It  is  generally  lie- 
lieved  that  the  currents  of  the  ocean  are  due  to  the  difference  in  tern- 


UNDULATIONS  IN  GASES.  205 

perature  and  density  of  its  different  parts,  aided  by  the  rotation  of   , 
the  earth  on  its  axis.  .Ar" 

381.  Undulations  in   aeriform  bodies.     Surface    waves, 
which  are  due  to  the  force  of  gravity,  may  be  produced  in 
gases  as  well  as  in  liquids.     Aeriform  bodies  are  also  subject 
to  undulations,  caused  by  their  elasticity,  which  are  called 
waves  of  condensation  and  rarefaction. 

If  the  piston  in  the  air  syringe,  Fig.  279,  be  driven  to  the  bottom 
of  the  cylinder,  and  the  pressure  be  suddenly  removed,  the  elasticity 
of  the  condensed  air  will  force  the  piston  upward.  If  there  were  no 
resistance  to  be  overcome,  the  inertia  of  the  air  would  cause  it  to 
expand  beyond  its  original  volume.  It  would  then  contract  again, 
and  thus  the  piston  would  be  made  to  oscillate  about  the  position  of 
repose.  In  the  same  way,  the  load  attached  to  the  weight  lifter,  Fig. 
148,  oscillates  by  the  alternate  rarefaction  and  condensation  of  the 
air  within  the  receiver. 

382.  The  same  phenomena  will  take  place  in  free  air. 
Let  a  soap  bubble,  containing  a  mixture  of  oxygen  and 
hydrogen,   be  exploded  by  the  flame   of  a   candle.      The 
vapor  formed  by  the  chemical  union  of  these  elements  fills 
a  sphere  many  times  greater  than  the   soap   bubble,   and 
thus  a  rarefaction  will  be  produced  at  the  center  of  disturb- 
ance.    The  pressure  of  the  surrounding  air  wrill  then  cause 
the  vapor  sphere  to  contract;  its  elasticity  will  again  impel 
it  outward,  and  thus  it  will  continue  to  oscillate  by  alternate 
rarefaction  and  condensation,  until  at  length  its  oscillation 
ceases. 

The  surrounding  particles  of  air  will  partake  of  these 
motions.  When  the  vapor  sphere  expands,  the  shell  of  air 
inclosing  it  will  be  condensed,  and  again  expand  as  the 
vapor  contracts.  This  aerial  shell  will,  in  like  manner,  act 
upon  a  second  exterior  shell ;  it,  in  turn,  upon  another,  and 
so  on.  Thus  the  initial  force  will  be  propagated  in  a  series 
of  alternate  condensations  and  rarefactions,  extending  in 
spheres  about  the  center  of  disturbance. 

These  movements  are  analogous  to  the  waves  on  the  sur- 
face of  liquids,  extending  in  circles  from  the  center ;  the 


206 


NATURAL    PHILOSOPHY. 


phase  of  elevation  corresponds  to  the  condensation,  and  the 
phase  of  depression   to  the   rarefaction.      An   aerial    wave 


consists  of  a  condensation  and  a  rarefaction.     Fig.  169  is 
an  attempt  to  represent  to  the  eye  four  aerial  waves. 

383.  The  propagation  of  aerial  undulations  will  be  best 
understood  by  considering  the  motion  of  the  particles  along 
one  of  the  rays  of  the  sphere,  as  a  x. 


a  b  c 


•x 

.x! 


.«'"r  r 

N  a""  //"' 


KM;.   170. 


Let  the  II|I|MT  line  <>f  «l».i-  rcpi-.-cnt   tin-  iiir  purticlrs  alon^  one  of 
the  radii,  in  a  state  of  rest,  :m<l  -U|.|M.M-  tin-  piirtirli',  a,  to  be  driven 


AERIAL    UNDULATIONS.  207 

toward  x,  so  as  finally  to  occupy  the  position  a',  in  the  second  line 
of  dots.  The  moment  that  a  begins  to  move,  its  impulse  begins  to 
IK-  transmitted,  by  the  elastic  force  between  the  particles,  to  6;  in  the 
following  moments  the  impulse  will  be  transmitted,  successively, 
through  6,cto  some  point,  as  o,  more  or  less  distant  from  a.  The 
particles  between  of  and  o/  are  all  compressed,  but  not  equally  ;  the 
condensation  is  greatest  at  a',  and  least  at  </. 

Now,  suppose  the  particle  of  to  have  reached  the  limit  of  its 
swing,  and  to  begin  to  return.  In  successive  moments,  the  particles, 
6'c',  etc.,  will  complete  their  vibration,  reach  their  greatest  conden- 
sation, and  then  follow  a  in  returning ;  while,  at  the  same  time,  the 
particles  beyond  o',  will,  in  turn,  be  set  in  vibration.  At  the  sup- 
posed rate  of  transmission,  when  the  particle,  a',  has  attained  its 
original  position,  at  a",  the  state  of  greatest  condensation  will  have 
reached  the  particles  at  o//,  and  a//n  will  constitute  a  wave  of  con- 
densation. 

The  inertia  of  the  returning  particles,  a",  6X/,  etc.,  will  now  carry 
them  beyond  a",  6/x,  etc.,  toward  a/x/.  The  greater  inertia  of  the  fore- 
most particles,  will  tend  to  separate  them  from  those  following,  so 
that  when  a/x  shall  have  reached  a//x,  o/x  will  have  resumed  its 
original  position,  and  the  particles  between  a///  and  o/x/  will  be  in  a 
state  of  unequal  rarefaction.  The  point  of  greatest  rarefaction  will 
be  at  ax//. 

When  the  particle  at  a//x  is  ready  to  swing  again  toward  x,  6//x 
will  have  reached  its  limit  and  the  point  of  greatest  rarefaction.  So, 
in  succession,  the  maximum  rarefaction  will  be  transmitted  through 
each  particle,  toward  x.  The  motion  is  evidently  that  of  a  progress- 
ive undulation,  which  will  continue  until  external  causes  bring  it  to 
rest.  The  length  of  a  rarefied  wave  is  aiv  r,  which  is  double  ax//  o/x/. 

The  distance  that  a  travels  toward  a',  depends  on  the 
intensity  of  the  disturbing  force,  and,  at  the  same  time, 
measures  the  degree  of  compression  of  the  wave.  The 
distance  through  which  any  particle  vibrates,  as  from  a'  to 
a",  is  called  the  amplitude  of  the  vibration.  The  motion 
to  and  fro,  as  from  a'  to  a'"  and  back,  constitutes  a  complete 
vibration.  The  length  of  an  aerial  undulation  is  the  dis- 
tance through  which  the  motion  is  transmitted  during  the 
time  of  a  complete  vibration.  It  consists  of  a  condensed 
and  a  rarefied  wave,  and  is  the  sum  of  the  distances  a"n 
-|-  aiv  r  —  aiv  iciv.  The  more  rapid  the  vibrations,  the  quicker 


208  NATURAL   PHILOSOPHY. 

the  waves  will  succeed  each  other,  and  the  shorter  will  be 
the  length  of  each  wave.  The  amplitude  of  the  vibration 
may  be  only  a  small  fraction  of  an  inch,  while  the  length 
of  an  undulation  may  be  many  feet.  The  greater  the  am- 
plitude, the  greater  will  be  the  alternate  condensations  and 
rarefactions,  and  the  greater  will  be  the  intensity  of  the 
wave. 

384.  The  velocity  with  which  undulations  are  transmitted 
through   aeriform    bodies   of  constant    temperature,    varies 
directly  as  the  square  root  of  their  elasticity,  and  inversely 
as   the   square   root   of  their   density.       So   long    as    these 
factors  are  unchanged,  all  waves  are  transmitted  with  equal 
velocity. 

Suppose  the  distance  the  undulation  traverses  in  a  second  to  be 
one  thousand  feet,  the  shorter  the  waves,  the  more  there  will  be  of 
them;  the  longer  the  waves,  the  fewer  their  number;  the  greater  the 
amplitude,  the  greater  will  be  the  resistance  to  be  overcome,  and 
vice  versa,  and,  by  consequence,  all  the  waves  will  move  over  equal 
spaces  with  equal  velocities. 

385.  What  has  been  shown  to  be  true  of  a  single  line 
of  particles,  applies  to  all  the  lines  extending  in  radii  from 
the    center    of    disturbance.       Consequently,   aerial    waves 
expanding   freely   form    spherical    surfaces,    continually   in- 
creasing,   and  thereby  involving  a  greater  number  of  par- 
ticles  in  their  motion.     The  intensity  of  a    wave   will  be 
diminished  in  proportion  to  the  space  over  which  its  motion 
is  diffused.     Therefore,  as  the   surfaces  of  spheres  are  as 
the  squares  of  their  radii: 

TV  uit<'n*itii  of  <i  iruri-  <li  nihtixjirx  an  the  square  of  the  dis- 
tance from  the  center  of  propagation  increases. 

This  law  is  inapplicable,  whenever  the  radial  diffusion  of 
the  wave  is  prevented  l»y  interposing  obstacles. 

386.  The  combination  and  interference  of  aerial  wave's 
follow   the    law-    alivadv  found    for  liquids.      If  confined   in 
tube-  and  pipes,  the  combination  of  the  direct  and  reflected 


REFLECTION  OF   WAVES. 


209 


waves  may  produce  nodes  and  stationary  undulations.  The 
meeting  of  two  waves  may  result  either  in  greater  conden- 
sation or  in  greater  rarefaction ;  or  the  waves  may  quench 
each  other,  wholly  or  partially,  according  to  the  algebraic 
sum  of  their  undulations. 

387.  The    reflection    of    waves    from    solid    surfaces    is 
governed  by  the  same  laws  that  apply  to  the  impact  of 
elastic  bodies,  i.  e.:  the  angles  of  incidence  and  reflection  will 
be  equal. 

Let  a  circular,  progressive  wave,  emanating  from  the  center,  O, 
strike  the  plane  surface,  S  B,  with  a  velocity  sufficient  to  have  carried 
it  in  .the  next  moment  to  S  P'  B.  The  particles  in  the  perpendicular 
ray,  O  O',  will  first  strike  the  sur- 
face, and  be  first  reflected  in  the 
direction,  O'  P.  When  the  di- 
verging rays,  O  D'  and  O  F,  reach 
the  surface,  they  will  be  reflected 
on  the  other  side  of  the  perpen- 
diculars, 3VF  E  and  M  K,  in  the 
lines,  O'D  and  O'L  Now,  as 
the  velocities  of  the  direct  and 
reflected  rays  are  the  same,  the 
reflected  wave  will  reach  the 
points  DPI,  in  the  same  time 
that  the  direct  wave  would  have  FlG 

arrived   at   the    points,   Dx  P' F, 

and  the  same  is  true  of  all  intermediate  points.  Hence,  the  reflected 
wave  proceeds  as  if  from  the  center,  O',  at  a  distance  from  the  sur- 
face, S  B,  equal  to  that  of  the  center  of  the  incident  wave,  O,  but  on 
the  opposite  side. 

388.  When  the  origin  of  the  wave  is  far  distant  from 
the  reflecting  surface,  the  waves  will  then   be  apparently 
rectilinear,  being  arcs  of  very  large  circles.     In  all  such 
cases,  the  diverging  rays,  falling  upon  small  surfaces,  may 
be  considered  parallel.     Parallel  rays,  incident  upon  plane 
surfaces,  will  also  be  parallel  after  reflection. 

389.  The  principles  of  geometry  enable  us  to  determine 
the  direction  of  waves  reflected  from  curved  surfaces.     We 

N.  P.  14. 


210 


NATURAL   PHILOSOPHY. 


may  regard  each  wave  as  made  up  of  an  indefinite  number 
of  linear  rays,  falling  upon  so  many  points  in  the  curve. 
Each  point  so  taken  constitutes  a  part  of  a  straight  line;  as, 
T  T',  tangent  to  the  curve  at  that  point.  As  every  radius 
is  perpendicular  to  the  tangent  at  its  extremity,  the  radii 
of  a  circle  constitute  so  many  perpendiculars,  which  we 
may  employ  in  laying  off  the  incident  and  reflected  angles 
in  circular  arcs. 

Suppose  a  rectilinear  wave  of  the  sea  to  enter  a  rocky  bay,  oi 
semicircular    shape.     As  each   portion   of  the    wave  in   turn    strikes 

the  rock,  it  will  be  reflected 
toward  a  point,  F,  half  way 
between  the  center  of  the 
bay  and  the  shore.  There 
will,  therefore,  be  a  com- 
mingling of  all  the  paral- 
lel 'rays  of  the  direct  wave, 
to  form  a  circular  wave, 
whose  center  is  this  common 
point.  The  interference  of 
the  direct  and  reflected  waves 
will  soon  "chop  up"  the 
bay  into  an  infinite  number 
FIG.  1:2.  °f  little  waves.  These  inter- 

fering waves  may  be  imitated 

by  allowinir  a  tiny  stream  of  mercury  to  trickle  from  a  pin  hole  in  a 
paper  cone  upon  a  basin,  containing  the  same  metal,  at  a  point  half 
way  between  the  center  and  circumference. 

390.  Lines  drawn  from   any  point   in   an  ellipse  to  the 

two  foci,  make  equal  angles 
with  the  tangent,  T  T'. 
These  angles  are,  therefore, 
complements  oi'  the  angles 
of  incidence  and  reflection, 
and  may  In-  used  in  their 
stead.  Hence,  waves  orig- 
173  inatin-  in  cilhcr  focus  of 

an     ellipse     \\ill     r,,ir 
after  reflection,   in  the  other  focus. 


VIBRATIONS.  211 

391.  Waves  diverging  from  the  focus  of  a  parabola  will 
be  reflected  from  the  surface  in  parallel  lines,  and,  conversely, 
waves    striking  the   parabola   in 
parallel  rays,  will  converge  after 
reflection  upon  the  focus.     It  is 
evident  that  two  parabolas  may 
so  face  each   other  that  rays  di- 
verging from  one  focus  shall  be 
made  to  converge  in   the  other. 


Reflecting  surfaces  thus  related  to  ^^ 

each  other  are  termed  conjugate.  FlG  174 

392.  Simultaneous  vibrations.  It  is  possible  to  subject 
the  cord,  in  Fig.  163,  to  transverse,  longitudinal,  and  tor- 
sional  vibrations  at  the  same  time.  Not  only  so,  but  the 
cord  may  be  made  to  vibrate  as  a  whole,  while,  at  the  same 
time,  it  is  vibrating  in  halves  and  thirds.  The  motion 
which  each  particle  assumes,  in  obedience  to  many  simul- 
taneous impulses,  is  very  complex,  but  each  impulse  pro- 
duces precisely  the  same  kind  of  vibration  as  if  it  were 
acting  alone.  The  possibility  of  many  independent  motions 
is  rendered  further  evident  by  the  movements  of  the 
heavenly  bodies  :  thus,  the  moon  revolves  (1.)  on  its  own 
axis;  (2.)  about  the  earth;  (3.)  with  the  earth,  about  the 
sun;  (4.)  with  the  sun  about  some  distant  center. 

Recent  investigations  have  made  it  probable  that  every  particle  of 
matter,  even  in  the  most  rigid  bodies,  is  constantly  in  motion,  and, 
it  may  be,  in  several  directions  at  the  same  time.  If  these  particles 
appear  to  us  in  a  state  of  rest,  it  is  only  because  our  senses  are  in- 
capable of  detecting  their  motion.  We  know  that  a  plant  increases 
in  size,  but  we  can  not  see  it  grow.  We  can  neither  see  the  motion 
in  the  hour  hand  of  a  watch,  nor  in  the  flight  of  a  bullet.  But  we 
know  that  the  plant,  the  hour  hand,  and  the  bullet  move,  by  the 
results  of  the  motion.  So  the  deductions  of  experiment  have  proved 
the  existence  of  many  motions,  too  obscure  to  be  easily  apprehended, 
and  apparatus  has  been  contrived  to  render  some  of  them  manifest 
to  our  senses.  Physicists  now  hold  that  all  phenomena  appreciable  by 
the  senses  are  the  results  of  different  modes  of  motion,  impressed  upon 


212  NATURAL   PHILOSOPHY. 

miitrrhil  particles.     Thus  we  may  have  the  following  modes  of  mo- 
tion: 

1.  Gross  mechanical  motion  of  machines. 

2.  The  regular  oscillations  of  pendulums  and  elastic  bodies. 

3.  Vibrations  resulting  in  the  sensation  of  sound. 

4.  Vibrations  resulting  in  the  sensation  of  heat. 

5.  Vibrations  resulting  in  the  sensation  of  vision. 

6.  Vibrations  producing  the  phenomena  of  electricity. 

7.  Movements  resulting  in  chemical  changes. 

8.  Finally,  we  hear,  taste,  touch,  smell,  and  see,  because  external  im- 
pressions   excite,   in    the    different    nerves,    vibrations,   which,    when 
transmitted  to  the  brain,  produce  all  our  sensations. 

393.  Recapitulation. 

There  are  two  varieties  of  waves : 

1 .  Waves  of  crests  and  hollows,  in  which  the  direction  of  displace- 
ment is  perpendicular  to  that  of  transmission.     This   is   exemplified 
by  waves  of  water,  the  undulations  of  light  and  of  heat. 

2.  Waves  of  condensation  and  rarefaction,  in  which  the  direction 
nf  displacement  coincides  with  that  of  transmission.     The  vibrations 
of  musical   instruments  are  transmitted  through  the  air,  to  the  ear, 
by  waves  of  this  sort,  which  are  therefore  called  sonorous  waves. 

We  are  justified  in  believing  that  all  our  sensations    are  due  to 
different  modes  of  motion  impressed  upon  matter. 


CHAPTER   VI. 


ACOUSTICS. 


394.  Hearing  is  a  sense  depending  upon  vibrations  excited 
in  the  auditory  nerve,  and  transmitted  to  the  brain.  The 
sensation  is  called  *ound.  Ex<-ej»t  in  case  of  disease,  the  sen- 
sation can  not  originate  in  the  nerve,  but  is  the  imjin  — inn 
(1.)  caused  by  the  vibrations  of  bodies,  (2.)  transmitted 


ACOUSTICS. 


213 


through  an  elastic  medium,  and  (3.)  conveyed  to  the  auditory 
nerve  by  the  mechanism  of  the  ear.  These  three  conditions 
are  always  requisite  for  the  sensation  of  sound. 

1.  Every  species  of  sound  may  be  traced   to  the  vibra- 
tions of  some  elastic  body. 

When  the  strings  of  a  violin  are  sounding,  the  transverse  vibrations 
appear  as  a  broad,  shadowy  surface.  When  a  tuning  fork  sounds, 
its  vibrations  may  be  felt  by  placing  one  of  its  prongs  lightly  upon 
the  teeth.  If  a  wire,  or  knife  blade  rests  against  the  edge  of  a  bell, 
or  a  glass  receiver,  when  ringing,  it  will  be  made  to  rattle.  The  sounds 
of  wind  instruments  are  due  to  the  vibrations  of  the  air  they  contain. 
The  tremors  produced  in  the  external  air  by  vibrations  of  an  organ 
pipe,  are  distinctly  perceptible.  Bodies  capable  of  producing  sound 
are  called  sonorous. 

2.  An  elastic  medium  is  required  for  the  transmission  of 
sound.     The  ordinary  medium  is  the  atmosphere. 

The  vibrations  of  sonorous  bodies  produce  in  the  air  waves  of  con- 
densation and  rarefaction,  which  correspond  in  rapidity  and  intensity 

to  the  rapidity  and  amplitude  of  the 
vibrations.  These  waves  succeed 
each  other  in  ever  increasing  spheres 
until,  at  last,  they  reach  the  ear. 
Two  or  more  media  may  be  employed 
in  transmitting  the  same  sonorous 
wave;  thus,  persons  in  a  close  room 
are  sensible  of  distant  sounds.  In 
such  a  case,  the  undulations  of  the 
external  air  cause  vibrations  in  the 
windows  and  walls,  which  produce 
corresponding  undulations  in  the  air 
within  the  room. 

If  a  bell,  kept  in  constant  vibra- 
tion by  clock  work,  is  supported  on 
a  thick  layer  of  loose  cotton,  under 
the  receiver  of  an  air  pump,  the 
sound  is  at  first  distinct,  being  con- 
veyed from  the  bell  through  the  air 
in  the  receiver  to  the  glass  and  the 
pump  plate,  and  thence  to  the  ear  by 
Fio.  us.  the  outer  air.  When  the  air  is  grad- 


214  NATURAL   PHILOSOPHY. 

ually  exhausted,  the  sound  grows  more  and  more  feeble,  and  ceases 
to  be  heard  when  a  vacuum  is  obtained. 

In  like  manner,  sound  is  quenched  by  the  interposition  of  any 
body  having  feeble  or  imperfect  elasticity.  Thus,  a  partition  filled 
with  sawdust,  or  covered  by  a  thick  carpet,  will  prevent  the  trans- 
mission of  sounds  from  one  room  to  another. 

3.  The  auditory  nerve  is  necessary  to  the  sensation  of 
sound. 

If  the  experimenter  is  deaf,  or  if  a  bell  rings  where  there  are  no 
hearing  organs  capable  of  perceiving  the  vibrations,  they  exist  merely 
as  sneh — without  producing  any  sensation. 

Sound  is  that  mode  of  motion  which  is  capable  of  affecting 
the  auditory  nerve.  Acoustics  is  the  science  which  treats  of 
the  cause,  nature,  and  phenomena  of  sound. 

395.  The  quality  of  sound  depends  on  the  elasticity  and 
form  of  the  sounding  body.     All  sonorous  bodies  are  elastic, 
but  all  elastic  bodies  are  not  sonorous.     Lead  is  not  sonorous, 
because  its  elasticity  is  too  imperfect  for  continued  vibrations. 
The  fibers  of  wool  and  cotton  are  highly  elastic,  but  are  not 
sonorous,  because  their  >li*i'n-ity  is  feeble,  so  that  their  vibra- 
tions are  slow  and  inaudible.     Steel,  glass,  silver,  brass,  and 
cat -gut  are   sonorous,   because   these   substances  are  highly 
Clastic,  and  possess  sufficient  force  for  rapid  vibrations. 

Edison's  phonograph  is  an  interesting  proof  that  sounds  are  due  to 
vibrations.  It  consists  of  an  elastic  plate,  to  the  center  of  which  a 
bard  stylus  is  so  attached  that  it  plays  above  a  sheet  of  tin-foil,  which 
is  made  to  cover  a  cylinder  whose  surface  is  cut  into  the  form  of  a 
screw.  On  turning  the  cylinder,  and  at  the  same  time  speaking  (it  the 
ela.-tic  plate,  the  stylus  forms  indentations  in  the  tin-foil  which  cor- 
r. -pond  to  the  sounds  uttered.  After  the  tin-foil  has  In-,  n  indented, 
if  the  cylinder  is  n-v«.lved  as  before,  the  sounds  will  be  reproduced  by 
tin-  elastic  membrane  with  greater  or  less  fidelity. 

396.  Quality  of  sound.     Noise  is  the  sensation  produced 
bv  unequal  "i%  confused   vibrations.      A    niu>ical  sound  is  pro. 
duccd    by    vibrations   ivrurriiii:  at    >lmrt  and   equal  intervals. 
If   the   vibrations    are    rapid,   the    sound    is    high,   or  acute; 


/.v77-:.v>vrr  OF  SOUND. 


215 


but  if   slow,  the  sounds  are  low  or  grave.     Therefore,  the 
pitch,  or  tone,  depends  on  tli<?  nipidity  of  the  vibrations. 

These  farts  may  IK-  shown  by  pressing  a  card  against  a  toothed  wheel 
in  motion.  If  such  a  wheel  be  attached  to  the  axis  of  a  whirling  table, 
or  a  gyroscope,  it  will  be  found  that  when  the  card,  E,  strikes  against 


FIG.  176. 

less  than  sixteen  teeth  per  second,  only  a  succession  of  taps  will  be 
heard,  but  if  the  number  exceeds  sixteen  per  second,  the  sounds 
blend  together  in  a  clear  musical  sound.  As  the  velocity  is  increased, 
the  sound  is  more  and  more  acute. 

The  number  of  vibrations  per  second  may  be  found  by  multiplying 
the  number  of  teeth  in  the  wheel  by  the  number  of  revolutions  the 
wheel  makes  per  second.  Sounds  are  in  unison  when  the  rapidity  of 
vibration  is  the  same.  The  rate  of  vibration  in  tuning  forks,  violins, 
and  other  musical  instruments,  may  be  found  by  making  the  wheel 
sound  in  unison  with  them.  The  same  thing  may  be  done  more  ad- 
vantageously by  the  syren,  which  is  a  wind  instrument  so  constructed 
as  to  register  the  number  of  vibrations  at  the  same  time  it  produces 
the  sound.  In  Savart's  wheel,  Fig.  176,  H  is  an  apparatus  which 
indicates  the  number  of  revolutions  in  the  toothed  wheel. 

397.  The  intensity  or  loudness  of  the  sound  depends  on 
the  amplitude  of  the  vibrations  ;  because  this  measures  the 
degree  of  condensation  of  the  sonorous  wave.  If  the  am- 
plitude is  large,  the  sound  is  intense,  or  loud;  but  if  small, 
the  sounds  are  feeble,  or  soft.  A  sound  may  maintain  the 


216 


XA  T  URA  L  PHIL  OS  OPHY. 


same  pitch  while  it  varies  in  intensity ;  thus,  a  tuning  fork 
continues  to  sound  the  same  tone  until  its  vibrations  are 
too  feeble  to  be  audible. 

The  intensity  of  sound  varies  inversely  as  the  square  of  the 
distance  of  the  sounding  body. 

This  is  because  the  undulations  form  spherical  waves  of  ever  in- 
creasing extent.  A  drum,  at  a  distance  of  one  hundred  feet,  sounds 
four  times  louder  than  at  two  hundred  feet,  and  one  hundred  times 
louder  than  at  one  thousand  feet.  For  this  reason,  loud  sounds  are 
propagated  further  than  feeble  ones.  The  sound  of  the  volcano, 
Tumbora,  was  heard  at  the  distance  of  eight  hundred  and  fifty 
miles. 

398.  When  a  string  vibrates  in  free  air,  it  emits  but  a 
feeble  sound ;  but  if  it  vibrates  above  a  sounding  box,  as 
in  the  case  of  a  violin,  guitar,  or  piano,  the  sound  is  much 
louder.  This  arises  from  the  fact  that  the  thin  plates  of 

the  box,  and  the  air  within 
them,  vibrate  in  unison 
with  the  string,  and  thus 
unite  to  form  sonorous 
waves  of  greater  intensity. 
Hence,  Sound  is  increased  in 
intensity  by  the  proximity  of 
a  resonant  body. 

This  effect  may  be  shown  by 
holding  a  vibrating  tuning  fork 
over  the  mouth  of  a  tall  glass 
jar,  and  carefully  pouring  water 
into  the  jar.  When  the  water 
tills  the  jar  to  a  certain  level, 
tin-  sound  of  the  fork  will  he 
greatly  inereast-d  l>y  the  vibra- 
tion of  the  column  of  air  within 
the  jar.  At  any  height  above 
or  below  this  level,  the  inten- 
sity of  the  sound  will  he  less- 
ened. The  length  of  the  air 

column   diniiiiMi.-s    u    ih.-    rapidity    <.f    vibration    increases,    and    is 
always  one-fourth  of  the  length  of  the  wave  produced  by  the  fork. 


Fio.  177. 


QUALITIES  OF  MEDIA.  217 

399.  Sympathetic  vibrations  are  always  produced  when 
one  sounding  body  vibrates  near  another  capable  of  emitting 
the  same  tone.     Thus,  if  the  voice  utters  a  prolonged  tone 
near  a  piano,  that  wire  will  be  set  in  vibration  whose  sound 
is  in  unison  with  the  pitch  of  the  voice.     By  changing  the 
pitch,  other  wires  will  respond.     This  is  because  the  sono- 
rous waves  excite  to  vibration  wires  which  are  capable  of 
vibrating  at  the  same  rate. 

400.  dualities  of  media.     The  experiment  in  (394)  proves 
that  sound  diminishes  in  intensity  as  the  air  is  rarefied.    If 
the   receiver  be  filled   with  other  gases,   it  will  be  found 
that  the  bell  has  a   feeble  sound  in  gases  lighter  than  air, 
as  hydrogen,  and  an   intense  sound  in  gases  denser  than 
air,  as  carbonic  acid.     Hence,  Hie  intensity  of  sound  depends 
on  the  density  of  the  medium  in  which  it  is  generated. 

These  experiments  are  confirmed  by  the  facts  that  the 
sound  of  a  pistol  fired  on  the  tops  of  high  mountains  re- 
sembles the  report  of  a  fire-cracker,  while  a  whisper  is 
painfully  loud  to  the  occupants  of  a  diving  bell  sunk  to  a 
considerable  depth.  The  energy  with  which  liquids  and 
solids  transmit  sound,  exceeds  that  of  the  atmosphere. 
Franklin  found  that  a  person  with  his  head  under  water 
could  hear  the  sound  of  two  stones  struck  together  at  the 
distance  of  half  a  mile.  The  scratch  of  a  pin  at  the  end 
of  a  long  stick  of  timber  seems  loud  to  a  person  whose  ear 
is  at  the  other  end. 

401.  Mixed  media.     If  the  lungs  be  filled  with  hydrogen, 
the  voice  is  weak   and  piping.     A  bell   under  a  glass  re- 
ceiver is  less  distinct  than  in  the  open  air,  although  glass  is 
among  the  best  conductors  of  sound.     A  noise  made  under 
water  is  feebly  heard  in  air,   and   vice  versa.      Hence,   the 
intensity  of  sound   i*  diminisJied  in  passing  from  one  medium 
to  another. 

The  conducting  power  of  air  is  diminished  when  it  is  disturbed  by 
alternating  currents  of  different  densities.  For  this  reason,  sounds 


218  NATURAL   PHILOSOPHY. 

are  less  distinct  by  day  than  by  ni^ht.  So,  also,  peals  of  thunder 
penetrate  to  a  less  distance  than  would  be  anticipated  from  their  in- 
tensity. 

402.  Limits   of  hearing.      All    ears    are   deaf  to   some 
vibrations.     The   gravest  sound   perceptible  to  the  human 
ear  is  produced  by  sixteen  complete  vibrations  in  a  second; 
the  highest  sound  is  caused  by  thirty-eight  thousand  com- 
plete  vibrations   in  a   second.     The   auditory   range  is   not 
the  same  for  all  persons.     Some  can  not  hear  the  highest 
notes  of  a   piano,   others  are  insensible  to   the  note  of  a 
cricket,    or  even   the   chirrup   of   a    house    swallow.      The 
hearing  of  these  persons  may  be  exceedingly  acute  within 
their  limit;    that  is,  they  may  be  able  to  distinguish  very 
feeble  sounds,  as  the  lowest  whisper. 

Naturalists  assert  that  many  insects  produce  sounds  that 
are  perfectly  appreciated  by  their  mates,  although  too  acute 
for  human  ears. 

403.  The  distance  at  which  sound  is  audible  varies  with 
it<  original  intensity  and  the  circumstances  which  modify  it. 

Still  air,  of  great  density  and  uniform  temperature,  is  favorable  to 
the  transmission  of  sound.  Under  ordinary  circumstances,  a  powerful 
voice  is  distinct  at  a  distance  of  seven  hundred  feet.  In  the  arctic 
regions.  Lieutenant  Foster  conver.-ed  with  a  sailor  at  the  distance 
of  a  mile  and  a  quarter.  The  cry  of  a  sentinel,  "All's  well,"  has 
been  conveyed,  in  still  air,  over  calm  water,  ten  miles.  Winds  and 
currents  increase  or  diminish  the  conducting  power  of  air,  according 
to  their  direction  and  force. 

Tin-  earth  transmits  sound  further  than  air.  The  cannonading  at 
Antwerp,  in  ls:Ji_'.  was  heard  in  the  mines  of  Saxony,  three  hundred 
and  twenty  miles  distant. 

404.  Acoustic   tubes.     If  the  sonorous  wave  is  not  per- 
mitted   to   expand,    its    intensity   can    lie    maintained    tor  a 
great  di>tance.       This  may  be  effected    bv  causing  the  wave 
to  pa-  through  a    tube.      Speaking    tubes    are    employed    in 

buildings  for  transmitting  messages  from  one  story  to 
another.     If  the  tube  terminate  in  a  suitable  sounding  box, 


VELOCITY   OF  SOUX1'.  219 

a  complicated  symphony,  played  hy  a  hand  in  the  basement, 
is  perfectly  transmitted  to  an  upper  hall,  though  inaudible 
in  the  intermediate  stones. 

405.  The  speaking  trumpets  employed   by  firemen   and 
mariners  reenforce  the  voice  by  the  vibrations  of  the  column 
of  air  contained   in  the  trumpet,  and  thus  increase  its  in- 
tensity.    The    hearing   trumpet  is   in   principle   the  same, 
though  its   form   is   the  reverse  of  the  speaking  trumpet. 
The  sonorous  wave  which  reaches  the  trumpet  transmits  its 
compression  or  rarefaction  to  portions  of  air  smaller  and 
smaller,    and   thus   transmits  it   with    increasing    intensity. 
The  form  of  the  external  ear  is  favorable  to  the  collection 
of  sound.     The  hand  held  concave  behind  the  ear  concen- 
trates the  sound  in  the  same  manner. 

406.  Velocity  of  sound.     Every  one  must  have  noticed 
that  the  flash  of  a  distant  gun  is  seen  before  the  report  is 
heard.     Experiments   based  on   this   observation    have   de- 
termined that  the  velocity  of  sound  in  still  air  at  32°  F.  is  one 
tln:"*nnd  and  ninety  feet  per  second.     The  velocity  increases 
as  the  temperature  rises,  at  the  rate  of  1.12  feet  for  every 
degree  Fahrenheit.     At  60°   F.,  sound  has  a  velocity  of 
eleven    hundred    and    twenty-one    feet    per    second.      The 
velocity  also  varies  with  the  direction  and  velocity  of  the 
wind. 

These  facts  enable  us  to  compute  the  distance  of  a  sound- 
ing body,  when  the  time  of  transmission  is  known.  When 
a  flash  of  light  accompanies  the  sound,  the  distance  may  be 
found  by  multiplying  the  velocity  of  sound  by  the  number 
of  seconds  that  elapse  between  the  flash  and  the  report. 

Thus,  if  when  the  air  is  at  80°  F.,  five  seconds  elapse  between  a 
flash  of  lightning  and  the  succeeding  peal  of  thunder,  the  stroke  is 
1150  X  5=  5750  feet  distant.  In  the  same  manner,  we  may  estimate 
the  height  of  a  cliff  by  dropping  a  stone  from  the  top  and  noting 
the  number  of  seconds  that  elapse  before  the  sound  is  returned  to 
the  ear.  Suppose  the  time  to  be  eight  seconds.  A  j>urt  of  the  time, 
r,  was  occupied  by  the  falling  body,  the  rest,  y,  by  the  sound ;  hence, 


220  NATURAL  PHILOSOPHY. 

x  +  y  =  8,  but  by  the  law  of  falling  bodies  x2  X  ISy?  equals  the 
height  of  the  cliff;  by  the  law  of  the  transmission  of  sound,  1090  y 
also  equals  the  height.  Hence,  z2.  16^  =  1090  y.  From  these  two 
equations  y  ~  0.77  -f  ;  therefore,  the  height  of  the  cliff  is  839.7  feet. 

407.  The  different  notes  simultaneously  produced  by  the 
instruments   of   an   orchestra    reach   the   ear   of  a   distant 
auditor  at  the  same  moment.     This  proves  that  all  sounds 
are  transmitted  wiifi  Hie  same  velocity  in  the  same  medium.     If 
this  were  not  so,  a  musical  performance  would  produce  only 
discords  to  all  except  those  in  the  immediate  vicinity. 

This  law  is  strictly  true  only  for  sounds  not  differing  greatly  in 
intensity,  for  it  has  been  noticed  that  the  report  of  a  cannon  is  some- 
times heard  before  the  command  given  to  fire.  Mathematical  inves- 
tigations also  lead  to  the  conclusion  that  a  very  intense  sound,  like  a 
peal  of  thunder,  is  transmitted  with  greater  velocity  than  a  gentler 
one. 

408.  The  velocity  of  sound  in  gases  is  directly  propor- 
tioned to   the  square  root  of  their  elasticity,  and  inversely 
as  the  square  root  of  their  density,     vccve-i-d.     This  is 
shown  by  the  following  table : 

Telocity  of  Sound  in  Gases  at  32°  f1. 

I'"t.  Feet. 


Air 1090 

Oxygen 1040 

Hydrogen  4164 


Carbonic  oxide 1107 

Carbonic  acid 858 

Protoxide  of  nitrogen 859 


In  this  table,  the  elasticity  and  density  are  due  to  the  pressure  of 
one  atmosphere.  By  Mariotte's  law  the  density  varies  with  the  elas- 
t icity,  so  that  any  decrease  in  density  is  counteracted  by  an  equal 
decrease  in  elasticity.  Therefore,  sound  will  move  up  or  down  a 
mountain,  or  at  any  altitude,  with  the  same  velocity  as  at  the  base, 
if  the  temperature  is  uniform.  The  effect  of  heat  on  gases  submitted 
to  a  constant  pressure  is  to  increase  their  elasticity  without  altering 
their  den.-ity.  Hence,  as  the  heat  is  generally  greater  at  lower  alti- 
tii'l.-,  tin-  velocity  of  -Diiinl  in  air  will  generally  be  greater  at  the 
sea  level  than  on  mountain  tops.  Newton  applied  these  facts  in  cal- 
culating the  velocity  of  sound  in  air.  The  velocity  obtained  by 
theory  is  about  one-sixth  less  than  that  found  by  experiment.  This 
discrepancy  is  due  to  the  fact  that  condensation  develops  heat,  and 


CO-EXISTENCE  OF  SOUNDS.  221 

rarefaction  produces  cold.  Hence,  the  condensation  of  the  sonorous 
wave  is  accomplished  with  greater  rapidity,  because  the  heat  devel- 
oped increases  the  elastic  force  between  the  particles ;  the  rarefaction 
of  the  wave  is  also  more  rapid,  because  the  cold  produced  diminishes 
the  elastic  force  to  be  overcome.  Therefore,  the  velocity  of  the  wave 
must  be  augmented  both  by  the  heat  and  by  the  cold  developed  in  its 
progress.  This  result  would  not  follow  if  the  heat  were  transmitted  to 
contiguous  particles. 

409.  The    velocity   of  sound  in  liquids   and    solids  is 
greater  than  in  air,  because   their  elastic  force  increases  in 
greater  ratio  than  their  density.     The  velocity  of  sound  in 
fresh  water  is  four  thousand  seven  hundred  feet  per  second. 
In  sea  water  it  is  a  little  more,  and  in  alcohol  nearly  one- 
fourth  less.     The  velocity  of  sound  per  second,  in  lead,  is 
four  thousand  and  thirty  feet;  in  silver,  five  thousand  seven 
hundred   and   seventeen   feet;    in   steel   and  glass,  sixteen 
thousand   six   hundred    feet;    in   pine,    ten   thousand   nine 
hundred  feet;    in  ash,  fifteen  thousand  three  hundred  and 
fourteen  feet. 

The  difference  of  velocity  in  solids  and  in  air  may  be 
demonstrated  by  placing  the  ear  at  one  end  of  a  long  bar 
or  wall,  while  an  assistant  strikes  a  blow  at  the  other  end. 
Two  sounds  will  reach  the  ear,  the  first  through  the  solid, 
and  the  other  through  the  air.  The  interval  between  them 
will  vary  with  the  length  of  the  solid.  The  approach  of  a 
railway  train  may  be  soonest  heard  by  applying  the  ear  to 
the  rail.  The  velocity  of  sound  varies  also  with  the  mole- 
cular structure  of  the  medium.  Wood  conducts  sound  in 
the  direction  of  its  fiber  two  or  three  times  faster  than 
across  the  grain. 

410.  Co-existence  of  sonorous  waves.    Many  sounds  may 
be  transmitted  at  the  same  time  in  the  same  medium  with- 
out modifying  each  other.     A  cultivated  ear   can   readily 
distinguish  the  sound  of  each   instrument  in   an   orchestra. 
This  i.<  analogous  to   the  little  waves  formed  on  the  large 
billows  of  the  ocean.     A  very  intense  sound  deafens  the  ear 
so  as  to  render  feeble  sounds  inaudible. 


222  XATURAL   PHILOSOPHY. 

411.  Combinations    of    sonorous    waves.      Many   feeble 
sounds   separately  inaudible,   may  unite  to   produce  a  sort 
of  murmur,   as   is   exemplified   in   tbe  rustle  of  leaves,  or 
the  hum   of  a  whispering   school.     Two   sonorous   waves, 
meeting  in   the  same  phase,  form   a  resultant  wave  of  in- 
creased intensity. 

412.  Interference  of  sonorous  waves.     If  two  sonorous 
waves  of  equal  intensity,  meet  in  opposite  phases,  both  are 
destroyed,    and    silence   results.      The    feeble    sound   of   a 
tuning  fork,  held  in  the  hand,  is  mostly  due  to  the  par- 
tial interference  of  the  two  waves  produced,  by  each  prong 
vibrating  in  an  opposite  direction.     If  a  tuning  fork,  when 
vibrating,  is  turned  slowly  round,  about   a  foot  from   the 
ear,  four  positions  will  be  found  in  which  the  interference  is 
total,  and  no  sound  is  heard. 

If  two  tuning  forks,  vibrating  respectively  two  hundred  and  fifty- 
five  and  two  hundred  and  fifty-six  times  in  a  second,  are  sounded 
together,  they  will,  at  first,  combine  to  produce  a  louder  sound  than 
either  could  alone,  for  both  generate  waves  in  which  condensation 
corresponds  with  condensation,  and  rarefaction  with  rarefaction.  At 
the  one  hundred  and  twenty-eighth  vibration,  one  will  have  gained 
half  a  vibration  on  the  other,  and  their  phases  are  in  complete  op- 
position and  there  will  be  no  sound,  because  the  condensation  of  one 
wave  is  neutralized  by  the  rarefaction  of  the  other.  For  the  next  half 
second,  the  interference  is  less  and  less,  and  at  the  end  of  the  second 
they  airain  combine.  At  every  even  nninbrr  of  half  seconds  the  sound 
will  be  doubled  in  intensity,  and  at  every  odd  number  dest  roved. 

This  alternate  combination  and  interference  is  known  to  musicians 
by  the  name  of  beats.  The  number  of  beats  in  a  second  is  always 
equal  to  the  difference  in  the  two  rates  of  vibration.  If  the  forks 
vibrate  in  unison  no  beats  will  be  heard.  If  one  vibrates  two  hun- 
dred and  fifty  and  the  other  vibrates  two  hundred  and  fifty-six  times 
in  a  second,  the  number  of  beats  will  be  six. 

413.  The  reflection  of  sound   is   in  accordance  with   the 
laws  already  deduced  for  the  reflection  of  wave.-.      (.'»N7.  ) 

A  sonorous  wave,  reflected  from  a  surface  of  <-OHH, In-able 
magnitude,  is  returned  to  the  ear  with  more  or  less  distincl- 
11688,  in  proportion  to  the  distance  of  the  .-urface.  The 


ECHOES.  223 

repetition  of  a  sound  by  reflection  is  called  an  echo.  Articu- 
late sounds  require  a  distance  of  one  hundred  and  nine 
feet  to  produce  a  distinct  echo,  because  the  voice  can  not 
utter,  nor  the  ear  hear,  more  than  five  syllables  in  a 
second. 

At  a  distance  of  one  hundred  and  nine  feet,  a  monosyllabic  echo 
may  be  perfect;  but  if  a  word  of  two  syllables  be  pronounced,  the 
echo  of  the  first  will  be  commingled  with  the  direct  sound  of  the 
second,  and  confusion  will  result.  At  a  distance  of  two,  three,  or  more 
times  one  hundred  and  nine  feet,  the  echo  will  be  dissyllabic,  trisyl- 
labic, and  so  on.  In  Woodstock  Park,  England,  is  an  echo  from  a 
reflecting  surface  twenty-two  hundred  and  eighty  feet  distant,  which 
returns  seventeen  syllables  by  day,  and  twenty  by  night. 

414.  Multiple  echoes  are  those  which  repeat  the  same 
sound  several  times.     This  happens  when  two  surfaces,  as 
parallel  walls,  reflect  the  sound  successively. 

An  echo  in  Italy  repeats  the  same  sound  thirty  times.  When  a 
cannon  is  fired  on  the  shores  of  Echo  Lake,  in  New  Hampshire,  the 
sound  is  reflected  from  a  succession  of  cliffs,  at  different  distances, 
and  produces  an  echo  like  a  peal  of  thunder.  The  reverberation  of 
thunder  is  also  due  to  echoes,  for  sound  is  reflected  not  only  from 
solid  surfaces,  but  also  from  clouds,  drops  of  water,  and  even  on 
passing  into  air  of  greater  density  than  its  own.  In  foggy  weather, 
sounds  are  rapidly  enfeebled,  because  they  undergo  so  many  partial 
reflections. 

415.  The  echo  may  be  heard  when  the  direct  sound  is 
inaudible.     Thus,  if  the  ear  be  placed  in  the  focus  of  a  con- 
cave mirror,   the  ticking  of  a  watch   may  be  heard  at  a 
distance,  when  it  would  be  otherwise  inaudible.     The  sound 
will  be  strengthened,  if  the  watch  be  also  placed  in  the  focus 
of  another  mirror,  opposite  to  the  first,  Fig.  174. 

The  same  effect  may  be  produced  in  rooms  having  smooth  walls 
of  a  continuous  curved  form.  In  such  a  chamber,  a  whisper  at  one 
focus  will  be  audible  at  the  other,  because  the  undulations  reflected 
from  the  different  points  of  the  walls  will  be  collected  at  the  other 
focus.  The  direct  rays  will  be  feeble  in  comparison,  and  on  this 
account,  two  persons  in  the  foci  could  converse,  and  yi-t  be  inaudible 
to  a  company  at  any  place  between  them.  Such  whispering  galleries 


224  NATURAL    PHILOSOPHY. 

are  not  uncommon.     The  dome  of  St.  Paul's  Cathedral,  London,  and 
of  the  Capitol,  at  Washington,  are  fine  examples. 

416.  Resonance.     The   increased  intensity   produced  by 
the  commingling  of  the  direct  and  reflected  sonorous  waves 
is  called  resonance.      Resonance   is   specially  noticeable   in 
empty  rooms,  with   bare  smooth  walls.     If  the  rooms  are 
small,  the  direct  and  reflected  waves  strike  the  ear  at  about 
the  same  time,  and  strengthen  the   original  sound  without 
diminishing  its  clearness. 

This  will  be  the  case,  if  the  echoing  walls  are  not  distant  more 
than  thirty-five  feet  from  the  speaker,  for  at  that  distance  the  reflected 
wave  will  go  and  return  in  one-sixteenth  of  a  second,  which  is  found  to 
be  the  limit  of  perceptibility.  Such  rooms  are  easier  to  speak  in 
than  the  open  air.  In  large  halls,  the  direct  and  reflected  waves  only 
partially  coincide,  and  the  words  are  less  distinct.  If,  however,  the 
echoes  are  quenched  by  the  furniture,  or  by  the  presence  of  an  audi- 
ence, the  direct  waves  only  are  heard,  and  the  words  are  distinct. 

Some  resonance  is  desirable,  if  the  room  is  very  large  and  the 
speaker's  voice  weak.  The  wall  behind  the  speaker  should  be  made 
ti>  aid  the  voice,  by  being  a  good  reflecting  surface  of  proper  shape. 
The  ceiling  should  not  be  too  high,  and  the  room  should  be  rather 
longer  than  broad.  The  echoes  from  distant  walls  should  be  broken 
up  by  galleries,  and  no  large  and  distant  surfaces  should  be  parallel 
to  nearer  ones. 

417.  Sound  may  also  be  refracted,   or  bent  out  of  its 
course,  in  passing  from  one  medium  to  another.     The  laws 
of  refracted  sound  are  the  same  as  those  of  light,  and  will 
be  treated  hereafter. 

418.  Recapitulation. 

1.  The  quality  of  sound  depends  on  the  elasticity  and  form  of  the 
.-.norous  body. 

2.  Tlu-  pitch  of  sound  depends  on  the  nito  of  the  vibrations. 

3.  The  intensity  of  sound  in<  i 

1.  With   the  amplitude  of  the  vibrations. 

2.  With  the  den-it y  of  the  ireneratint;  medium. 
.",.    My  the  proximity  of  a    n-,,n:int  body. 


MUSICAL  SOUNDS.  225 

The  intensity  of  sound  decreases 

1.  As  the  square  of  the  distance  increases. 

±  In  passing  from  one  medium  to  another. 
Is  maintained  or  strengthened  by  acoustic  tubes. 

4.  The  velocity  of  sound   is  not  dependent  on   quality,   pitch,  or 
intensity,  but  varies  with  the  elasticity  and  density  of  the  medium. 

(  (1)  May  co-exist  in  the  same  medium. 

5.  Sonorous  waves  4  (2)  May  combine  and  interfere. 

(_  (3)  May  be  reflected  or  refracted. 

MUSICAL    SOUNDS. 


419.  The  ear  recognizes  all  sounds  of  pure  tone  as  agree- 
able.   Nearly  thirty -eight  thousand  different  sound  waves  are 
possible,  each  one  of  which  will,  by  itself,  produce  a  pure 
tone.     If  all  these  were  produced   in   succession,  the  most 
practiced  ear  would  be  able  to  distinguish,  as  distinct  tones, 
less  than  the  one-hundredth  part  of  them.     This  is  because 
two  tones,  whose  rates  of  vibration  are  nearly  the  same,  can 
be  distinguished  from  unison  only  by  the  formation  of  beats. 
If  the  beats  are  not  readily  perceptible,  the  ear  recognizes 
the  sounds  as  the  same.     Any  tone  may  be  selected  for  a 
basis  of  comparison,  to  which  all  others  are  either  higher 
or  lower. 

420.  Suppose  a  guitar  string,  or  wire,  to  be  stretched 
across  a  sounding  box,  of  the  form  represented  in  Fig.  178, 
which   is   called   the   sonometer,    or   monochord.      When   the 
whole  length  of  the  string  vibrates,   it  produces  a  sound 
called   the  fundamental    tone   of   the    string.      It    may,   of 
course,  be  any  one  of  the  thirty-eight  thousand  perceptible 
tones.     Suppose  the  tone  to  be  that  due  to  one  hundred 
and  twenty-eight  complete  vibrations  in  a  second,  as  meas- 
ured by  the  toothed  wheel  or  the  syren.     Musicians  have 
agreed  to  designate  this  tone  as  Cj.     It  corresponds  to  C, 
in  the  second  space  of  the  base   clef.     If,  now,  the  bridge, 
B,  be   placed  at   half  the  length   of  the   string,    the   half 

N.  P.  15. 


226  NATURAL   PHILOSOPHY. 

string  will  make  two  hundred  and  fifty-six  vibrations  in  a 
second,  or  twice  as  many  as  the  fundamental.  The  tone 
produced  is  C2,  which  corresponds  to  middle  C  of  the 


piano.  If  the  string  be  again  shortened,  by  placing  the 
bridge  at  one-fourth  its  length,  the  number  of  vibrations 
will  be  again  doubled,  and  the  new  tone,  C3,  will  corre- 
spond to  C,  in  the  third  space  of  the  treble  clef,  due  to  five 
hundred  and  twelve  vibrations  per  second. 

Every  successive  halving  of  the  string  will  double  the  rate 
of  vibration,  and  produce  in  succession  C4,  C5,  and  so  on. 
On  the  other  hand,  if  strings  be  taken  two,  four,  eight  times 
the  length  of  the  original  string,  the  rates  of  vibration  will 
be  diminished  in  the  ratio  one-half,  one-fourth,  one-eighth, 
and  produce  respectively  the  tones  C_,,  C_2,  C_3,  corre- 
sponding to  sixty-four,  thirty-two,  and  sixteen  vibrations  pel- 
second.  If  these  tones  were  produced  in  succession,  the 
relation-  between  vibrations  of  the  strings  are  represented  by 
the  numbers  1  :  2  :  4  :  8  :  16  :  32,  etc. 

The  ratio  between  any  two  tones  is  called  an  interval, 
ami  indicates  how  much  one  sound  is  higher  than  another. 
The  interval  1  :  2  which  exists  between  the  tones  of  the 
Beriee  found  is  called  an  octave,  because  between  any  two 
tonei  hearinir  this  ratio,  other  tones  having  simple  relations 
may  be  placed,  so  as  to  form,  with  the  two  extremes,  a  series 
of  ri'jht  -oiimU  having  airreealile  relations  to  each  other. 


421.  These  eight  tones   constitute  the   diatonic  scale  or 
gamut,   in   music.      They  are   designated    by   the    first    seven 


DIATONIC  SCALE.  227 

letters  of  the  alphabet.  If  the  length  of  the  string  which 
sounds:  the  fundamental  be  assumed  as  1,  the  relative  length 
required  to  produce  the  other  tones  of  the  scale  are : 

Tones CDEFGAB         C 

Relative  length  of  cord I        I        f        I        I        f        A        i 

The  relative  number  of  vibrations  corresponding  to  these 
tones  is  expressed  by  the  reciprocals  of  these  numbers,  as 
follows : 

Tones CDEFGAB        C 

Relative  No.  of  vibrations..  1         f         f         t         f         f         V5         2 

Therefore,  (1.)  The  number  of  vibrations  per  second  is  in- 
>•>  I'M-ly  proportioned  to  tJie  length  of  the  string. 

These  tones  may  also  be  produced  by  increasing  the  ten- 
sion of  the  string,  without  altering  its  length.  This  may 
be  done  by  increasing  the  weights,  P,  by  which  the  string  is 
stretched.  To  double  the  number  of  vibrations,  the  stretch- 
ing weight  must  be  quadrupled. 

Tones CDEFGAB        C 

Relative  stretching  weight..  1       f£      f  f       V5        f        V       *££       4 

Therefore,  (2.)  The  number  of  vibrations  per  second  varies 
as  the  square  root  of  the  weight  by  which  the  string  is  stretched. 

As  the  elastic  force  of  a  string  is  dependent  both  on  its 
density  and  diameter,  these  functions  modify  the  rate  of 
vibrations  produced  by  strings  of  the  same  length  and  ten- 
sion. Their  combined  effect  determines  the  weight  of  a 
string.  A  string  four  times  as  heavy  as  another,  makes 
but  half  the  number  of  vibrations. 

Tones CDEFGAB        C 

Relative  weight  of  string....  1        ff       |f      T95        f        &       £&      \ 

Hence,  (3.)  The  number  of  vibrations  per  second  varies  in- 
>••  ra  ///  as  the  square  root  of  the  weight  of  a  given  length  of 
string. 


228  NATURAL    PHILOSOPHY. 

All  these  laws  may  be  proved  by  tin-  sonometer.  All  are  applied 
in  the  construction  of  stringed  instruments.  A  bar})  or  piano  is  a 
good  example.  The  high  notes  are  produced  by  short,  thin  strings; 
the  low  notes  by  long,  heavy  ones;  the  strings  are  brought  to  the  proper 
pitch  by  tension,  applied  at  the  pegs. 

422.  The  absolute  number  of  vibrations  per  second  in 
any  tone  may  be  found  by  multiplying  the  number  found 
for  C,  by  the  fractions  f,  f,  etc.,  which  express  the  rela- 
tive number.     Thus,  the   upper  octave  of  the  base  clef  is 
produced  by  the  following  series : 

Tones Cj     Dx     E:     Fa      Gj     AJ      Bj      C2 

Absolute  No.  of  vibrations..  128    144    160    170|    192    213£    240    256 

The  absolute  number  of  vibrations  in  the  higher  scales  is  obtained 
by  multiplying  these  numbers  by  two,  four,  eight,  etc.,  while  for 
lower  scales  the  same  numbers  are  divided  by  two,  four,  eight.  Thus, 
the  number  of  vibrations  of  A3  is  213£  X4  —  853£  in  a  second. 

The  actual  number  employed  by  orchestras  in  different  cities  is  not 
the  same.  For  this  reason  a  congress  of  musicians  has  adopted  the 
following  scale,  which  gives  all  the  tones  of  the  lower  octave  of  the 
treble  in  whole  numbers. 

Tones C2      D2     E2     F2     G2      A2      B2      C3 

New  scale  of  vibrations 264    297    330    352    396     440    495    528 

423.  The  length  of  a  sonorous  wave  may  readily  be  found 
by  dividing  the  velocity  with  which  sound  travels  in  a  second 
by  the  number  of  vibrations  in  the  same  time.     In  air  at 
60°  F.,  sound  moves  about  eleven  hundred  and  twenty-one 
feet  per  second.     The  length  of  the  wave  C,  is,  therefore, 
1121  -4-  128  =  8.7  feet.     C2  =  4.3  feet,  C4  =  1.1  feet.     It 
must   lie  borne  in  mind  that  the  length  of  the  wave  varies 
with  the  medium  and  the  temperature. 

424.  The  interval    between    any    two    tones   is   called    a 
musical  interval.     Musical  intervals  an-  named  by  the  order 
of  their  position  with  respect  to  any  note  taken  as  the  fun- 
damental, as  seconds,  thirds,  fourths,  etc.     The  interval  of 
the  fifth,  a<  C(J,  or  (J  I)2,  is  expressed   l»y  the  ratio  3  :   2, 
or  £.     The  numerical  value  of  any  interval  is  obtained  by 


MUSICAL  SCALE. 


229 


dividing  the  number  of  vibrations  in  a  given  tone  by  the 
mimlH-r  of  vibrations  in  that  preceding  it.  The  table  on 
this  page  is  a  summary  of  the  results  already  obtained  for 
two  octaves  of  the  diatonic  scale. 


W- 


& 


o 


4 


. 

t-    OQ  pq 


"3       N 

OQ    O 


<S 


l~-         ro 

-rfi  . 


fc  - 


IH*H    o 
3     *H  ^r<    «H-  co 

jc    ^  pq  ,-H 

a  a«*:*3 


1   1  |  1 

g       M    ^    <! 


230  NATURAL    PHILOSOPHY. 

The  interval  between  any  two  successive  notes  is  called  a  scale  in- 
terval. There  are  three  scale  intervals:  the  major  tout',  f,  between 
CD,  FG,  or  A  B;  the  minw  tune,  ',;',  between  D  E  or  G  A  ;  and  the 
major  or  diatonic  semitone,  jf,  between  EF  or  B  Co.  The  interval 
found  by  dividing  a  minor  tone  by  the  major  semitone  is  railed  the 
minor  or  chromatic  semitone.  Its  value  is  V  -=-  If  =  I  f  >  an(l  is  the 
least  interval  usually  regarded  in  music.  Any  less  interval  is  called 
a  comma,  though  this  term  is  more  specifically  applied  to  the  ratio 
between  a  major  and  minor  tone  f  -r-  y  =  f  J.  When  two  tones  differ 
only  by  a  comma,  they  are  generally  reckoned  as  of  the  same  value 
in  music,  consequently  the  intervals  f  and  ^  are  taken  as  whole 
tones  of  equal  value,  and  the  intervals  }  -;  and  ri  ,'  as  equal  semitones, 
although  they  differ  respectively  by  f^  and  yff. 

The  interval  between  C  E,  F  A,  or  G  B,  contains  two  whole  tones, 
and  is  called  a  major  third;  its  value  is  f  X  V  =  !•  The  interval 
between  EG,  AC2,  or  BD2,  contains  one  whole  tone  and  one  semi- 
tone, and  is  called  a  minor  third;  its  value  is  f  X  If  =  f  •  The  in- 
terval, DF,  differs  from  a  minor  third  only  by  a  comma;  y  X  if  X 


425.  The  pleasure  derived  from  music  depends  on  the 
frequent  recurrence  of  vibrations  in  the  same  phase.  When 
different  tones  are  produced  in  close  succession,  or  simul- 
taneously, the  effect  on  the  ear  will  be  more  or  less  agree- 
able, according  us  the  relations  between  their  vibrations  are 
simple  or  complex.  If  the  ratio  between  any  two  sets  of  vi- 
brations can  be  expressed  by  whole  numbers,  less  than  five  or 
six,  the  combination  will  be  pleasant. 

Melody  is  due  to  the  succession  of  single  tones,  having 
agreeable  relations  to  each  other.  The  air  in  a  piece  of 
music  is  an  example  of  melody. 

A  chord  is  due  to  the  simultaneous  production  of  two  or 
more  tones  in  agreeable  relations  to  each  other.  A  harnnniii 
is  a  melodious  succession  <>f  chords.  The  air,  in  music,  with 
the  accompaniment,  constitutes  a  harmony. 

Notes  in  unison  are  agreeable,  IMT.IU-C  their  vibrations  an-  coinci- 
dent throughout.  Next  in  order  is  the  chord  of  the  octave,  because 
every  alternate  vibration  of  the  higher  tone  coincides  with  the  funda- 
mental, in  the  same  phase.  Then  follow  in  turn  the  iifth,  the  fourth, 
the  major  third,  and  the  minor  third.  The  second  and  seventh  are 


CHORDS.  231 

by  no  means  equally  pleasant,  because  the  coincidences  are  less  fre- 
quent. Below,  is  an  attempt  to  represent  the  relations  between  the 
simple  chords.  The  dots  represent  the  rarefaction  of  the  wave,  the 
lines  the  condensation ;  the  long  lines  mark  coincidences  in  the  phase 
of  condensation. 


Unison.     1  :  1.     As  CC. 


Octave.     2:1.     As  CC2,  DD2.  gj| 

Fifth.     3  :  2.     As  CG,  FC2.  g  | 

Fourth.    4:3.     As  C  F,  AD2.  £  | 

Major  third.     5:4.     As  C  E,  F  A.  §  |  •  'l*-'  I  '•",•'  I  '  ! 

Minor  third.     6:5.     As  E  G,  A  C2  g  I 


426.  Compound    chords    are    formed    of  three  or   more 
tones,  which,  when  taken  two  and  two,  are  harmonious.    A 
perfect  major  chord  consists  of  three  simultaneous  tones,  such 
that  the  first  and  second  form  a  major  third,  the  second  and 
third  a  minor  third,  and  the  first  and  third  a  perfect  fifth. 
Thus  CEG   or  FAC2  constitute  a  perfect  major  chord, 
because  their  intervals  taken  two  and  two  are   C  E  f ,  EG 
|,  C  G  %.    The  ratios  of  this  triad  are  very  simple,  4:5:6, 
and  the  number  of  coincident  vibrations  very  many.     If  the 
same  intervals  are  taken  in  the  order  of  a  minor  third,  major 
third,  and  perfect  fifth,  the  tones  form  a  perfect  minor  chord. 
Thus,  DFA  or  EGB  ascend  in  the  order  DF  -J,  FA  }, 
D  A  f ,  and  form  a  perfect  minor  chord. 

427.  The  diatonic  scale  is  composed  of  unequal  intervals, 
because  this  disposition  of  the  vibrations  is  found  to  result 
in  a  greater  number  of  concords  than  would  be  possible  if 
the   intervals  were   all   equal.     The   scale   has   two  modes. 
In  the  first,  which  is  the  most  common,  the  first  third  is  a 
major  third  ;  in  the  other,  the  first  third  is  a  minor  third  : 
consequently,   the   modes    are  denominated  the    major  and 
the  minor  mode. 


232  .V.I  TURAL   PHILOSOPHY. 

The  intervals  in  both  scales  are  the  same,  though  not  in  the  same 
order.  If  the  diatonic  scale  begins  with  C,  the  mode  is  major,  and 
the  semitones  occur  in  the  third  and  seventh  intervals.  If  the  dia- 
tonic scale  begins  with  A,  the  mode  is  minor,  and  the  semitones 
are  found  in  the  second  and  filth  intervals.  Because  the  ear  seems 
to  require  that  the  seventh  interval  should  always  be  a  semitone, 
there  is  this  additional  peculiarity  in  the  minor  mode,  that  the 
seventh  note  is  sharped,  so  as  to  make  the  last  interval  a  semitone, 
as  in  the  major  mode.  The  sixth  interval  thereby  becomes  a  tone 
and  a  half.  The  sharped  seventh  is  called  the  accidental  seventh, 
and  is  considered  essential  to  the  minor  mode  in  the  ascending  scale. 

428,  Musicians  interpolate  other  notes  in  the  scale  by 
means  of  sharps  and  flats,  which  are  indicated  by  the  signs 
$  and  fc.  A  note  is  sharped  or  flatted  by  multiplying  its 
value,  respectively,  by  ff,  or  by  ff.  The  tone  of  the  note 
is  thereby  raised  or  lowered  a  chromatic  semitone.  If  the 
lower  note  of  the  interval  of  a  minor  tone  is  sharpened,  or 
the  higher  note  flattened,  the  reduced  interval  is  a  diatonic 

semitone.     Thus : 

D        D»       Efe        E 

t. .  *i  .  t   "; J 

The  interval,  D  Efr  or  D#  E,  is  ff ,  a  diatonic  semitone. 
D#  and  E|j  are  not  identical,  but  because  they  differ  only 
by  a  comma,  they  are  considered  equivalent  in  music.  The 
difference  between  the  interpolated  sharp  and  flat  in  the 
interval  of  a  major  tone,  as  F#  Gfc,  is  nearly  equal  to  a 
chromatic  semitone.  Upon  instruments  capable  of  modula- 
tion, as  the  violin  or  flute,  they  are  not  played  alike  by  a 
skillful  performer,  in  solo  pieces. 

Upon  instruments  with  fixed  keys,  the  accurate  rendcriii- 
of  .-harps  ami  Hats  would  require  a  key-hoard  so  large  as 
to  be  exceedingly  inconvenient.  For  this  reason,  all  the 
whole  tones  are  made  equal  and  divided  into  two  equal 
semitones,  so  that  the  sharp  of  one  tone  is  made  identical 
with  the  flat  of  the  next  higher.  The  octave  is  thereby 
divided  into  twelve  equal  intervals,  called  clir<>in<iti<-  temi- 
tme*,  and  forms  the  chromatic  scale,  namely: 
C,  C*  or  Db,  D,  D*  or  Eb,  E,  F,  Ff  or  Gb,  G,  G*  or  Ab,  A,  AS  or  lib,  B,  C. 


TRANSPOSITION.  233 

In  this  system,  all  the  intervals,  except  that  of  the  octave,  differ  more 
or  less  from  their  true  value,  but  the  errors  are  so  distributed  through 
the  scale  that  each  note  is  sufficiently  correct  for  practical  purposes. 
The  white  keys  of  the  piano  produce  the  adjusted  diatonic  scale; 
the  black  keys  the  interpolated  sharps  and  flats.  There  is  no  black 
key  between  E  F  or  B  C,  because  the  interval  between  them  is  a 
semitone;  so  that  E8  equals  F,  Ffe  equals  E,  Bf  equals  C,  and  Cb 
equals  B. 

429.  Transposition.  The  musical  scale  which  has  C  for 
its  fundamental  is  called  the  natural  scale,  or  the  key  of  C. 
It  is  evident  that  whatever  be  the  fundamental  tone  of  a 
string  vibrating  as  a  whole,  it  may  be  divided  so  as  to  form 
the  relative  intervals  of  the  octave.  Other  scales  are  thereby 
formed  which  take  their  names  from  the  fundamental,  as, 
key  of  G,  key  of  D,  etc.  The  same  result  may  be  accom- 
plished by  means  of  flats  and  sharps,  so  interpolated  as  to 
preserve  the  same  relative  intervals  between  the  successive 
tones.  The  relations  of  the  octave  in  the  major  mode  are 
thus  indicated: 


Key  of  C  C 

D 

E 

F 

G 

A 

B         C2 

Name  of  in-  )  1 

2 

3 

4 

5 

6 

7           8 

tervals.       I  Do 

re 

mi 

fa 

sol 

la 

si          do 

Intervals  

Tl.   •                        t    !    , 

DA 

semi- 

trmA            tn 

HA             t.r 

iTIP            ID 

semi- 
np          form 

The  first  three  intervals  of  an  octave  are  the  same  as  the 
last  three.  Consequently,  the  fifth  of  any  scale  may  be 
taken  as  the  fundamental  of  the  new  scale.  Therefore,  the 
first  transposition  from  the  natural  scale  is  to  the  key  of  G. 

Key  of  G G      A      B      C2     D2     E2     Ffl2     G2 

Do    re     mi     fa      sol      la      si       do 

If  G  be  taken  as  the  fundamental,  all  the  intervals 
succeed  each  other  in  the  required  order,  as  far  as  the 
sixth,  E  F,  which  is  naturally  a  semitone.  F  is,  therefore, 
.sharped,  to  make  the  sixth  interval  a  whole  tone.  The 
seventh  interval,  F#G,  thereby  becomes  a  semitone,  and 


234  NATURAL   PHILOSOPHY. 

the  octave  is  complete.     The  second  transposition  is  to  the 
key  of  D. 

Key  of  D D      E      FS     G      A      B      C*      D 

Do     re      mi      fa      sol      la       si      do 

Here  C  is  sharped  to  make  the  seventh  interval  a  semi- 
tone. A  note  once  sharped  remains  so  in  successive  trans- 
positions; hence,  the  key  of  D  contains  two  sharps,  F£  and 
C#.  Other  transpositions  by  sharps  follow  in  the  order,  C, 
G,  D,  A,  E,  B,  FJf. 

The  scale  may  be  also  transposed  by  flats,  by  taking  in  succession 
the  fourth  tone  above  the  fundamental,  as  the  new  key  note.  Thus: 

Key  of  F F      G      A       Biz     C      D      E      F 

Do     re      mi      fa      sol      la      si       do 

In  this  case  the  third  interval  is  naturally  a  whole  tone,  but  is 
made  a  semitone  by  flattening  B ;  the  fourth  interval,  Bb  C,  thereby 
becomes  a  whole  tone,  as  is  required. 

430.  Harmonics.     We  have  seen  (392)  that  a  cord  may 
be  made  to  vibrate,  either  as  a  whole  or  in  any  number  of 
parts.     It  is  impossible  to  sound  the  cord  as  a  whole  with- 
out, at  the  same   time,  producing,  in  a  greater  or  less  de- 
gree,   the   vibrations    of  its    aliquot    parts.      There    results 
from  this  a  commingling  of  the  fundamental  tone  with   it- 
higher  harmonic  tones.     There  is  the  same  coexistence  of 
different  vibrations  in  all  sounding  bodies.     This  intermix- 
ture of  tones  determines  the  timbre  or  quality  of  the  musical 
HHind,  and   enables   us   to   distinguish  one   musical    instru- 
ment from  another;   thus,  a  violin  and  flute  sounding  the 
same   fundamental    are   not   confounded,    because   the   har- 
monics of  the;  first  are  different  from  those  of  the  other. 

431.  Musical  instruments  maybe  grouped  in  three  divis- 
ions.     (1.)   Instruments  in  which  a   tense  membrane   is  the 
source    of    vibration  ;    as    the    drum    and    tambourine.      (2.) 
Stringed  instrument.-,   in  which  the  sounds  produced   by  the 
vibrations  of  coed-  aiv  M  renirtliened  by  a  resonant    box  ;    as 
the  violin  and  piano.      (3.)  Wind  instruments,  in  which  the 


WIND   INSTRUMENTS. 


235 


sound  is  due  only  to  a  column  of  air  confined   in   sonorous 
tubes;  as  the  flute  and  clarionet. 

432.  The  material  of  which  the  sonorous  tube  is  made 
has  no  influence  on  the  pitch  of  the  sound,  although  it 
modifies  the  timbre  in  a  striking  manner.  This  is  probably 
due  to  the  production  of  harmonics  by  a  very  feeble  vibra- 
tion of  the  tubes  themselves.  With  reference  to  the  man- 
ner in  which  the  air  is  made  to  vibrate,  sonorous  tubes  are 
divided  into  (1.)  mouth  pipes  and  (2.)  reed  pipes. 

Fig.  179  represents  the  mouth-piece  of 
an  organ  pipe.  The  aperture,  lb,  is 
called  the  mouth,  and  6 a,  the  lips.  When 
a  blast  of  air  is  forced  through  the  aper- 
ture, /,  it  strikes  against  the  lip,  6,  which 
partially  obstructs  it,  and  causes  the  air 
to  issue  from  6  a  in  an  intermittent  man- 
ner. In  this  way,  pulsations  are  pro- 
duced, which  are  transmitted  to  the  air 
within  the  pipe,  and  a  sound  is  the  re- 
sult. 

Fig.  180  represents  a  reed  pipe,  made 
from  a  wheaten  straw,  by  raising  a  strip 
of  straw  near  a  joint.  On  blowing  into 
this  opening  the  reed  vibrates  and  com- 
municates its  pulsations  to  the  air  in 
the  straw,  and  produces  a  musical  sound. 
The  sound  produced  depends,  in  general, 
on  the  dimensions  of  the  pipe  and  the 
velocity  of  the  current  of  air.  Thus,  a 
shriller  note  will  be  produced  if  the  force 
of  the  blast  is  increased,  or  if  the  tube  is  shortened.  The  reed  re- 
mains the  same,  but  is  forced  to  vibrate  at  the  same  rate  as  the  col- 
umn of  confined  air. 


FIG.  179. 


FIG.  180. 


433.  The    absolute   length    of    pipes.      The    sounds    of 
pipes   are   due   to   waves   of  condensation   and    rarefaction 


236  NATURAL   PHILOSOPHY. 

which  are  transmitted  through  the  length  of  the  pipe. 
Nodes  and  segments  will  be  formed,  as  in  the  case  of  vi- 
brating strings. 

1.  In  a  stopped  pipe,  the  closed  end  will  always  be  a  node,  because 
the  air  particles  are  necessarily  at  rest,  although  they  undergo  rapid 
alternations  of  condensation   and   rarefaction.     At   the   mouth-piece, 
the  air  particles  will  undergo  no  changes  in  density,  since  they  are 
always   in  contact  with   the  external  air,  but  will  have  the  greatest 
amplitude   of   vibration.     This   point,  therefore,   corresponds  to   the 
ventral  segment,  and  the  stopped  pipe,  sounding  its  fundamental  tone, 
is  one-half  of  a  condensed  or  of  a  rarefied  wave  in  length. 

2.  In  an  open  pipe,  both  ends  are  always  ventral  segments,  because 
the  column  of  air  inclosed  is  in  contact  with  the  external  air  at  those 
points.     Hence,  when   the  pipe  sounds  its  fundamental,  a  node  will 
be  formed  at  the  center  (N,  Fig.  179).     The  air  column  will,  there- 
fore, equal  in  length  a  wave  of  condensation  or  of  rarefaction ;   that 
is  to  say,  one-half  of  a  sonorous  wave.     (383.)     Hence,  also,  the  fun- 
damental tone  of  a  tube,  open  at  both  ends,  is  an  octave  higher  than 
a  stopped  pipe  of  the  same  length. 

434.  Now,  as  the  velocity  of  sound  in  air  is  eleven  hun- 
dred and  twenty-one   feet  per  second,  and  as  a  continuous 
sound  can  not  be  produced  by  less  than   thirty-two  single 
vibrations  per  second,    the   maximum   length  of  an   open 
pipe  is  i'l1     =35  feet.     A  closed  pipe,  producing  the  same 
tone,  will  be  half  that  length,  or  17.5  feet.     With  a  gentle 
blast  of  air,  low  C  of  the  treble  clef,   which  corresponds  to 
two  hundred  and   fifty-six  complete  vibrations  per  second, 
will  be  produced  by  a  stopped  pipe  thirteen  inches  long,  or 
by  an  open  pipe  twenty-six  inches  long. 

The  velocity  of  sound  in  different  gases  and  liquids  may  be  com- 
puted by  fun-ing  them  through  properly  constructed  organ  pipes,  and 
by  finding  the  length  of  the  pipe  which  must  be  used  with  each  in 
order  to  yield  a  given  tone. 

435.  By  increasing  the  blast  of  air  in  a  stopped  tube,  the 
column   divides   in   three  equal  parts,  and  an  intermediate 
node,  N',  and  sj-iriin-nt,   $',  are  formed;   a  second   increase 
produces  another  node-  and  segment,  and  so  on.     Therefore, 


RECAPITULA  TION. 


237 


the  same  stopped  pipe  may  be  made  to  produce  in  succession 
the  fundamental  and  it.<  uneven  harmonics,  whose  vibrations 
are  in  the  series,  1,  3,  5,  7,  etc. 

If  the  tube  be  open  at  both  ends,  the 
first  harmonic  will  be  produced  by  divid- 
ing the  column  into  four  equal  parts,  by 
nodes  and  segments,  Fig.  181.  The  sec- 
ond by  forming  six  equal  parts,  and  so 
on.  Therefore,  the  same  open  pipe  may 
be  made  to  produce  in  succession  the  fun- 
damental and  its  harmonics,  whose  vibra- 
tions are  in  the  natural  series  of  numbers, 
1,  2,  3,  4,  etc. 

436.  The  flute,  fife,  flageolet,  are  mouth 
pipes ;  the  clarionet  and  hautboy  are  reed 
pipes.    On  opening  one  of  the  holes  at  the 
sides,  a  segment  is  formed  at  that  point, 
which  modifies  the  distribution  of  nodes  and 
segments  in  the  interior,  and  thus  changes 
the  tone.     The  trumpet  and  trombone  are  reed  instruments, 
in  which   the  lips  of  the  performer  take  the  place  of  the 
reed,  and  vibrate  in  the  mouth-piece.     In   the  organ,  both 
reed  and  mouth  pipes  are  used. 

437.  Recapitulation. 

1.  Any  sonorous  body  may  be  made  to  yield  a  pure  tone. 

2.  The  tone  chosen  as  the  fundamental  is  determined  by  the  prac- 
tice of  the  best  musicians,  and   the  corresponding  number  of  vibra- 
tions ascertained. 

3.  The  pleasure  derived  from  music  is  due  to  a  succession  of  melo- 
dious or  harmonious  tones. 

4.  The  diatonic  scale  contains  eight  tones,  of  different  intervals. 

5.  The   relative   number   of  vibrations   in   an   octave   may  be  ex- 
pressed  by  a   simple   series.     The   corresponding  tones   may  be  ob- 
tained by  varying  the  length,  tension,  and  weight  of  strings;  or  by 
varying  the  length  of  sonorous  tubes  and  the  force  of  the  blast. 


FIG.  181. 


238  NA  TURA  L    PHIL  OSOPH  Y. 

6.  The  chromatic  scale  contains  twelve  equal  intervals,  obtained  by 
interpolating  sharps  and  flats  in  the  diatonic  scale. 

7.  The  transposition  of  the  scale  is  effected  by  making  its  funda- 
mental tone  higher  or  lower,  and  still   preserving   the  natural  series 
of  intervals. 


CHAPTER   VII. 

OIPTICS. 

438.  LIGHT  is  that  mode  of  molecular  motion  which  ex- 
cites in  us  the  sensation  of  vision.     Light  affects  all  nature: 
it  influences  chemical  action,  it  is  necessary  to  the  growth 
of  plants,   and   it   unfolds   to  our  eyes   the   knowledge  of 
external  things. 

439.  The  wave  theory  of  light  assumes,  (1.)  that  matter 
of  extreme  rarity  and  elasticity,  called  the  luminiferous  aetfier, 
pervades  all  space,  even  the  interstices  between   the   mole- 
cules   of   every    substance.      (2.)    That   the    molecules    of 
luminous   bodies   are   in   a   state   of   very   rapid   vibration. 
(3.)  That  these  vibrations  are  communicated  to  the  aether 
and  are  then  transmitted  in  all  directions  by  spherical  waves. 
And  (4.)  that  these  waves  or  vibrations  constitute  light. 

440.  A  medium  is  any  substance  through  which  light  is 
transmitted:    as  gla>s,  horn.      Tr<tn*i>nrrnl  bodies  allow  light 
to  pass  freely  through    them;   as  glass,   water,   air.      7'/v///x- 
lucent  bodies  transmit   light   so  imperfectly  that  objects  can 
not    be   clearly  seen    through   them  ;   MS  ground  glass,  horn. 
Opaffue   bodies   do    not    transmit    light;    as    wood    and    the 
metals. 

441.  Luminous  bodies  are  those  in  which  light  originate-; 
as  the  sun  and  burning  bodies.     Non-luminous  bodies  origi- 


SOURCES   OF  LIGHT.  239 

nate  no  light,  luit  may  be  rendered  temporarily  luminous 
l»y  the  presence  of  a  self-luminous  body;  thus,  a  lighted 
candle  renders  adjacent  objects  luminous. 

442. a  The  sources  of  light  are  (1.)  mechanical  action, 
(2.)  chemical  action,  (3.)  electricity,  (4.)  phosphorescence, 
and  (5.)  the  heavenly  bodies. 

Any  solid,  on  being  raised  to  977°  F.,  begins  to  emit 
light,  of  a  dull,  red  color,  and  is  then  said  to  be  incandes- 
cent. The  light  of  incandescent  bodies  varies  with  the  in- 
tensity of  the  heat.  At  1280°  F.  it  is  bright  red;  at  1440° 
F.,  blue;  at  2000°  F.,  orange;  at  2130°  F.,  white;  and  it 
continues  to  increase  in  brilliancy  above  this  temperature. 
A  current  of  gas  does  not  become  luminous  at  2000°  F. 

Mechanical  action  may  produce  sufficient  heat  to  render 
solids  incandescent.  Thus,  sparks  of  light  are  produced 
when  flint  and  steel  are  struck  violently  together.  M»>i 
artificial  lights  depend  on  the  ignition  of  solid  particles  in 
the  intense  heat  developed  by  chemical  action.  If  oxygen 
and  hydrogen  are  burned  together  an  intense  heat  is  pro- 
duced, but  the  light  is  feeble,  because  the  product  of  the 
combustion  is  gaseous.  If,  however,  a  solid,  as  a  bit  of 
lime,  is  held  in  the  flame,  it  becomes  incandescent,  and 
emits  a  light  of  great  intensity. 

In  ordinary  combustion,  the  hydro-carbons  contained  in 
the  oil,  coal,  gas,  etc.,  are  decomposed  by  the  heat;  the 
hydrogen  then  burns  with  a  pale  flame  ;  into  this  flame  the 
solid  particles  of  the  carbon  rise,  become  incandescent,  and 
finally  burn. 

The  transient  light  of  the  electric  spark  and  the  brilliant 
glare  of  lightning  are  familiarly  known,  but  electricity  may 
be  made  to  furnish  a  continuous  and  abundant  supply  of 
light 

Phosjihorescence  is  a  pale  light,  emitted  in  the  dark,  with- 
out any  manifestation  of  heat.  The  light  of  the  glow- 
worm and  the  fire-fly  are  examples.  In  tropical  climates, 
the  sea  is  often  covered  with  a  bright  phosphorescence,  due 


240  NATURAL   PHILOSOPHY. 

to  extremely  small  animalculse.  Under  certain  conditions, 
rotten  wood  and  decaying  flesh  become  phosphorescent. 
Phosphorescence  may  also  be  developed  in  some  minerals  by 
heat,  friction,  and  crystalization. 

The  cause  of  the  light  of  the  sun  and  the  fixed  stars  is 
unknown,  but  the  prevailing  opinion  is  that  it  is  due  to 
some  form  of  mechanical  action.  The  moon  and  the 
planets  are  non-luminous;  receiving  from  the  sun  the  light 
by  which  they  shine. 

442b.  The  velocity  of  light  was  first  ascertained  by 
Roemer,  by  means  of  the  eclipses  of  the  first  satellite  of 
Jupiter.  Jupiter  is  a  planet  attended  by  four  moons  which 
revolve  about  it,  as  our  moon  revolves  about  the  earth. 
These  moons  are  observed  by  the  telescope  to  undergo  fre- 
quent eclipses,  by  passing  behind  the  body  of  the  planet. 
The  exact  moment  when  the  moon  becomes  eclipsed,  as 
would  be  seen  by  a  spectator  at  the  mean  distance  of  the 
earth  from  the  sun,  is  calculated  by  astronomers. 

Both  the  earth  and  Jupiter  revolve  about  the  sun,  but  in 
different  periods;  consequently,  they  are  sometimes  on  the 
same  side  of  the  sun,  and  sometimes  on  opposite  sides.  In 
the  former  case,  the  earth  is  about  one  hundred  and  eighty- 
three  millions  of  miles,  or  the  whole  diameter  of  its  orbit, 
nearer  to  Jupiter  than  in  the  latter.  Now,  it  is  found  by 
observation,  that  the  eclipse  of  the  first  moon  is  seen  about 
16fJ  minutes  sooner  when  the  earth  is  nearest  to  Jupiter 
than  when  it  is  most  remote  from  him;  therefore,  the  light 
must  occupy  this  time  in  crossing  the  earth's  orbit.  The 
velocity  of  light  is  then  about  one  hundred  and  eighty-five 
thousand  five  hundred  miles  in  a  second. 

The  velocity  of  light  has  also  been  determined  by  direct 
'•\|M-riment,  and  found  to  vary  in  different  media;  being, 
in  water,  one  hundred  and  forty-four  thousand  miles  per 
second;  in  glass,  one  hundred  and  twenty-eiirht  thousand 
miles  ;  and  in  diamond,  seventy-seven  thousand  miles. 

443a.  Luminous  bodies  may  he  considered  as  a  collection 


SHADOWS.  241 

of  luminous  particles,  or  points.  A  luminous  point  may 
be  seen  in  all  positions  of  the  eye,  if  no  opaque  body  in- 
tervenes ;  hence,  light  radiates  in  aU  directions  from  every 
luminous  point.  A  single  line  of  light  is  called  a  ray.  A 
l»  ncll  of  light  is  a  collection  of  rays  from  the  same  source. 
The  rays  of  a  pencil  naturally  tend  to  separate  from  each 
other,  or  to  become  divergent;  but  they  may  be  so  modified 
as  to  pass  through  a  common  point,  or  become  convergent; 
hence,  we  may  have  diverging  pencils  and  converging  pencils 
of  light.  A  collection  of  rays  which  are  sensibly  parallel 
is  called  a  beam  of  light. 

In  a  homogeneous  medium  light  moves  in  straight  lines,  for  if 
an  opaque  body  be  placed  in  a  direct  line  between  the  eye 
and  the  luminous  point,  the  light  is  intercepted.  A  ray  of 
sun  light  admitted  into  a  dark  room  is  seen  to  be  straight, 
by  illuminating  the  floating  particles  of  dust  in  its  course. 

443b.  Shadows.  When  light  falls  on  an  opaque  body,  the 
space  behind  the  body,  from  which  light  is  excluded,  is 
called  the  shadow. 

If  the  source  of  light  be  a 
luminous  point,  the  shadow  will 
be  bounded  by  the  rays  tangent  FlG  ]84. 

to  the  surface  of  the  body.     A 

section  of  the  shadow  received  on  a  screen  will  increase  in 
breadth  in  proportion  to  the  distance  of  the  screen. 

If  the  source  of  light  have  a  sensible  magnitude,  the 
opaque  body  will  cast  an  independent  shadow  for  each 
pencil  of  luminous  rays. 

Let  AB,  Fig.  185,  represent  a  luminous  body,  and  CD  the 
section  of  an  opaque  body.  The  pencil  from  the  luminous 
point,  A,  will  be  intercepted  between  the  lines,  CF  and  DH, 
and  the  pencil  from  B  will  be  intercepted  between  the  lines, 
C  E  and  D  F.  Hence,  all  the  light  will  be  excluded  only 
between  the  lines,  CF  and  D  F,  which  inclose  the  true 
shadow,  or  umbra. 

The  space  beyond,  between  the  lines,  C  E  and  C  F,  and 

N.  P.  16. 


242 


NA  T  URA  L  PHIL  OS  OP II Y. 


between  DF  and  D  H,  receives  light  from  certain  points 
of  the  luminous  body,  and  not  from  others.  It  is  brighter 
than  the  true  shadow,  but  not  so  bright  as  the  illuminated 
space,  and  is,  therefore,  called  the  partial  shadow,  or  pe- 
numbra. 


FIG.  185. 

If  the  luminous  body  is  smaller  than  the  opaque  object,  the  shadow 
will  be  larger  than  the  body;  thus,  if  the  hand  be  held  near  a 
candle,  a  gigantic  shadow  of  the  hand  may  be  thrown  on  a  distant  wall. 
If  the  luminous  body  is  larger  than  the  opaque  object,  the  breadth  of 
the  umbra  will  gradually  diminish  to  a  point,  but  the  breadth  of  the 
penumbra  will  increase  with  the  distance  to  which  it  is  thrown. 

444.  Images  formed  by  direct  light.  If  luminous  rays 
are  transmitted  through  a  small  aperture  into  a  dark  room, 
and  are  then  received  on  a  screen,  they  form  inverted 
images  of  external  objects.  The  luminous  rays  proceed  in 
straight  lines ;  those  from  the  top  of  the  object,  Fig.  186, 
are  received  on  the  bottom  of  the  screen,  and  those  from 
the  base  of  the  object  on  the  top  of  the  screen.  The  rays 
of  light,  therefore,  must  cross  each  other  without  interfer- 
ing. A  darkened  room,  so  arranged,  is  one  form  of  the 
camera  obscura. 

A  single  luminous  point  will  give  an  image  the  shape  of 
the  aperture;  if  the,  aperture  is  triangular,  the  image  will 
be  triangular.  Hence,  a  luminous  body  will  give  an  infi- 
nite number  of  superimposed  triangular  images;  the  union 
of  all  these  partial  images  produces  a  total  image  of  the 


INTENSITY  OF  LIGHT. 


243 


same  form  of  the  luminous  object.  Therefore,  the  image  is 
independent  of  the  shape  of  the  aperture,  if  the  latter  is 
sufficiently  small.  The  image  will  be  indistinct  if  the  aper- 
ture is  large,  or  if  the  screen  is  too  far  removed.  It  will  be 
distorted  if  the  screen  is  not  perpendicular  to  the  direction 
of  the  rav>. 


FIG.  186. 

In  accordance  with  these  principles,  the  images  of  the  sun  which 
are  formed  on  the  floor  when  its  light  is  transmitted  through  small 
openings  in  the  blinds,  are  round  or  elliptical,  according  to  the  incli- 
nation of  its  rays  to  the  floor.  Similar  images  are  formed  on  the 
ground  by  the  solar  light  passing  through  the  dense  foliage  of  a 
forest.  During  an  eclipse  the  images  will  be  more  or  less  of  a  crescent 
shape,  in  proportion  to  the  obscuration  of  the  sun. 

445.  The  intensity  of  the  light  varies  inversely  as  the 
square  of  the  distance  from  the  luminous  point.  Suppose  a 
luminous  point,  or  the  flame  of  a  small  candle,  to  be  placed 
in  the  center  of  a  hollow  sphere;  the  whole  interior  surface 
of  the  sphere  will  be  lighted  by  the  candle.  Now,  since  the 
surfaces  of  spheres  are  as  the  squares  of  their  radii,  each 
square  inch  of  the  surface  will  receive  four  times  as  much 
light,  if  the  sphere  have  a  radius  of  one  foot  than  if  its 
radius  were  two  feet,  and  nine  times  more  than  with  a 
radius  of  three  feet. 


244 


NA  TURA L    PHIL  OS01 '// ) . 


This  law  may  be  proved,  experimentally,  by  shadows.  A  board 
having  a  surface  one  foot  square,  placed  one  foot  from  a  candle,  will 

cast  a  shadow  that  will  cover 
four  square  feet  at  double 
the  distance,  nine  square  feet 
at  three  times  the  distance, 
and  so  on.  The  areas  in- 
crease as  the  square  of  t he- 
distance,  and,  consequently, 
the  intensity  of  light  on  each 
square  inch  will  decrease  in 
proportion  to  the  square  of 
the  distance  from  the  lumin- 
ous  point. 

446.  The  relative  in- 
tensities   of   two    lights 

may  be  compared  by  an  application  of  this  law.  Place  an 
opaque  rod  before  a  vertical  screen  of  white  paper,  or  of 
ground  glass,  and  arrange  the  lights  so  that  each  shall  cast 
;i  shadow  of  the  rod  on  the  screen.  Now  move  one  of  the 
lights  backward  or  forward,  until  a  position  is  obtained  in 
which  both  the  shadows  appear  equally  dark.  If  the  shadows 
are  sensibly  equal,  the  amount  of  light  falling  on  the  screen 
from  each  source  must  be  equal  also;  the  relative  intensities 
of  the  two  lights  are  then  found  by  squaring  the  distance 
of  each  light  from  the  screen. 

The  light  which  we  receive  from  the  sun,  at  a  distance  of  ninety- 
one  million  miles,  is  equal  to  the  concentrated  glare  of  five  thou- 
sand five  hundred  and  sixty -three  wax  candles  at  the  distance  of  a 
foot.  The  light  of  the  full  moon  is  three  hundred  thousand  times 
less  than  that  of  the  sun.  The  brightest  of  the  fixed  stars  shines 
with  only  one  twenty-thousand-millionth  part  of  the  light  which  we 
receive  from  the  sun.  For  this  reason,  tin-  stars  arc  invisible  when 
the  sun  shines,  being  lost  in  his  superior  brilliance. 

447.  The  visual  angle  is  the  angle  contained  between 
two  lines  drawn  from  the  center  of  the  eye  to  the  two  ex- 
tremities of  the  object.  (1.)  For  the  same  distance,  the 
visual  angle  increases  with  the  size  of  the  object.  (2.)  For 


DISTANCE  AND   SIZE. 


245 


the  same  object,  the  angle  decreases  with  the  distance  of  the 
object ;  thus,  if  the  same  object,  A  B,  is  removed  to  A'  B', 


the  visual  angle  decreases.  Hence,  if  the  size  of  an  object 
is  known,  we  may  estimate  its  distance  by  its  visual  angle, 
having  learned,  by  experience,  to  associate  together  distance 
and  angular  size. 

448.  The  optic  angle  is  the  angle  contained  between  two 
lines  drawn  from  a  luminous  point  through  the  centers  of 
the  two  eyes  when  they  are  both  directed  to  the  same  point. 


FIG.  189. 


The  optic  angle,  BAG,  increases  with  the  nearness  of  the 
object.  We  may  judge  of  the  relative  distance  of  an  ob- 
ject by  the  muscular  effort  required  to  turn  our  eyes  so  as 
to  direct  them  toward  the  object.  Nevertheless,  this  power 
comes  only  from  long  experience,  as  persons  born  blind, 
whose  sight  has  been  restored  by  a  surgical  operation,  im- 
agine, at  first,  that  all  objects  are  at  the  same  distance. 

449.  Our  estimate  of  distance  is  more  correct  when 
many  objects  intervene;  the  stars  overhead  all  appear  at 
the  same  distance,  because  we  have  no  standard  for  compar- 
ison. Finally,  the  more  distinct  an  object  is,  the  nearer  it 
seems  to  be.  Distant  mountains,  if  seen  for  the  first  time 
in  pure  air,  appear  nearer  than  they  really  are,  and  the 
reverse  if  the  air  is  foggy. 


246  NATURAL  PHILOSOPHY. 

450.  Our  estimate  of  size  is  closely  associated  with  our 
judgment  of  distance.     If  the  object  is  unknown,  we  form 
an   estimate   of   its    distance   by   comparison   with    that   of 
known  objects,  and  then  estimate  its  size  by  the  visual  angle. 
Any  thing  that  increases  our  estimate  of  distance  also   in- 
creases our   estimate   of   size.      The   moon   appears   larger 
near  the  horizon  than  when  above  us,  because  it  seems  more 
distant  by  reason  of  intervening  objects.     So,  also,  objects, 
seen  in  a  fog,  often  appear  enormously  large,  because  they 
appear  to  be  distant  by  reason  of  their  indistinctness. 

451.  Disposition    of  incident   light     When  a  pencil  of 
light   falls   on   any   substance,    it   is   separated    into    parts. 
(1.)  Some  of  the  rays  are  absorbed.     (2.)  Some  are  reflected, 
and   (3.)  some  may  be  transmitted,  or,  with  more  or  less 
change  in  direction,  refracted. 

Absorption.  A  very  thin  plate  of  glass  is  almost  perfectly 
transparent,  but  as  its  thickness  is  increased,  its  transparency 
is  diminished,  and  it  may  be  made  so  thick  as  to  transmit  no 
light.  Eacli  thin  layer,  therefore,  weakens  the  vibrations,  so 
that,  if  they  pass  through  a  certain  number  of  layers,  the 
undulations  become  so  feeble  as  to  be  insensible. 

Even  the  purest  air  absorbs  so  much  light  that  the  atmosphere 
would  not  transmit  the  rays  of  the  sun,  if  it  had  the  depth  of  seven 
hundred  miles.  On  the  other  hand,  gold  may  be  made  so  thin  as  to 
transmit  light  of  a  violet-green  color. 

452.  Recapitulation. 

I.  Bodies  are  classified,  in  accordance  with  their  relations  to  light, 
in  regard 

1.  To  the  emission  of  rays {  Luminous. 

(  Non-luminous. 

("Transparent. 

2.  To  the  transmission  of  rays <  Translucent. 

(.  Opaque. 

f  1.    Altsnrl>r<l. 

II.  Light,  incident  on  a  surface,  is J  2.   KtfKrt.d. 

(  :;.   Transmitted. 


CATOPTRICS.  247 

REFLECTION    OF    LIGHT,    OR   CATOPTRICS. 

453.  Whenever  a  pencil  of  light  falls  on  a  body,  some 
portion  of  it  is  reflected,  or  thrown  back  into  the  medium 
it  was  just  leaving. 
If  a  ray  of  light, 
IB,  falls  on  a  plane 
surface,  AC,  it  will 
be  reflected  in  the 
line,  B  R.  Draw 
the  line,  P  B,  per- 
pendicular to  the  re- 
flecting surface,  at 

the    point    of   inci-  FIQ 

dence,  B.  The  an- 
gle, IBP,  is  called  the  angle  of  incidence.  The  angle,  PBR, 
the  angle  of  reflection.  If  these  angles  are  carefully  measured, 
it  will  be  found  that 


1 


Tlie  angle  of  incidence  is  equal  to  the  angle  of  reflection. 

2.  The  incident  and  reflected  rays  are  both  in  tfie  same  plane, 
which  is  perpendicular  to  the  reflecting  surface. 

454.  These  laws  apply  to  every  reflecting  point  of  inci- 
dence. There  may  be  two  modes  of  reflection:  (1.)  when 
a  pencil  of  light  falls  on  an  unpolished  surface,  the  re- 
flected rays  are  scattered  in  every  direction,  and  are  said  to 
be  irregularly  reflected,  or  diffused.  (2.)  When  a  pencil  of 
light  falls  on  a  perfectly  polished  surface,  the  reflected  rays 
proceed  in  a  determinate  direction,  and  are  said  to  be  regu- 
larly reflected. 

When  examined  by  the  microscope,  most  flat  surfaces  are  found  to 
consist  of  an  infinite  number  of  minute  planes,  inclined  to  each  other 
in  all  possible  angles,  and,  therefore,  capable  of  receiving  and  reflect- 
ing light  in  all  possible  directions ;  by  the  operation  of  polishing, 
these  irregularities  of  surface  are  so  much  reduced  that  very  many 
points  of  incidence  lie  in  the  same  plane,  and  the  light  reflected  from 
them  will  proceed  in  the  same  direction. 


248  NATURAL   PHILOSOPHY. 

455.  Non-luminous  bodies  are  rendered  visible  by  light  irregularly 
reflected.     Bodies  not  in  the  direct  sunlight,  are  illuminated  by  the 
(litliiM/d  light  reflected  from  the  air,  the  clouds,  and  the  surrounding 
objects. 

If  a  sufficient  portion  of  incident  light  is  regularly  reflected,  the 
eye  may  perceive  an  image  of  the  body  which  emits  the  light.  A 
tarnished  mirror  will  reflect  a  dim  image  of  an  object  by  regularly 
reflected  light,  and  is  itself  visible,  in  all  its  parts,  by  irregular  reflec- 
tion. On  polishing  the  mirror,  more  light  is  regularly  reflected,  and 
the  image  becomes  brighter ;  but  no  mirror  can  be  so  highly  polished 
that  it  will  diffuse  no  light,  for  then  the  mirror  would  itself  be  invis- 
ible. So,  also,  no  substance  can  absorb  or  transmit  all  the  light 
which  falls  upon  it,  for  the  blackest  body,  or  the  most  transparent,  is 
still  visible. 

456.  The  intensity  of  reflected  light  increases  (1.)  with 
the  degree  of  polish;    (2.)  with  the  angle  of  incidence,  except 
in  case  of  the  metals.     A  sheet  of  writing  paper  will  reflect 
an  image  of  a  candle,  if  the  eye  be  held  close  to  the  paper 
so  as  to  receive   the  reflected  rays  very  obliquely,  but  not 
otherwise. 

(3.)  The  intensity  of  reflected  light  varies  with  the  nature  of 
the  reflecting  substance.  In  polished  metals,  the  reflection  is 
almost  perfect;  in  charcoal,  it  is  almost  wanting.  A  common 
looking-glass  reflects  light  both  from  the  anterior  surface 
of  the  glass,  and  from  the  amalgam  of  tin  with  which  it  is 
coated  on  the  back.  In  good  mirrors,  the  superior  inten- 
sity of  the  image  from  the  metallic  surface  overpowers  the 
faint  image  from  the  anterior  surface  of  the  glass ;  but  in 
mirrors  badly  coated,  both  images  may  be  seen. 

The  regular  reflection  of  waves  of  light  follow  the  general  laws  of 
undulations  already  considered  in  pages  209,  210.  Some  further 
details  are  necessary  in  order  to  understand  the  formation  of  imag.-s 
in  mirrors. 

457.  Mirrors   am   either  plane  or  curved.      An   ordinary 

lookini:-Lrla>s  is  an  example  of  a  plain-  mirror.  The  most 
common  kind-  of  curved  mirrors  an-  those  whose  eurvature 
is  spherical.  A  convex  spherical  mirror  is  a  portion  of  the 
surface  of  a  spin-re,  reflecting  light  from  the  external  face: 


PLANE  MIRRORS. 


249 


FIG.  192. 


a  concave  spherical  mirror,  is  a  portion  of  the  surface  of  a 
sphere  reflecting  light  from  the  internal  face. 

458.  The  formation  of  images  by  plane  mirrors  may  be 
determined  by  investigating  the  images  due  to  a  series  of 
points.     Let   M  N  be   a  plane   mir- 
ror, and  A  a  luminous  point.      The 

reflected  rays  will  make  the  same 
angles  with  the  perpendiculars,  D  P, 
as  the  incident  rays,  and  hence  the 
reflected  rays  will  make  the  same 
angles  with  each  other  as  they  did  be- 
fore reflection,  but  will  appear  to  di- 
verge from  the  point,  A'.  By  an  easy  geometrical  construc- 
tion, it  may  be  shown  that  if  a  pencil  of  rays,  diverging  from 
a  luminous  point,  fall  on  a  plane  mirror,  ike  reflected  rays  will 
appear  to  diverge  from  a  point  similarly  placed  behind  Hie  mir- 
ror, and  at  a  distance  equal  to  that  of  the  luminous  point  before 
the  mirror. 

Of  the  great  number  of  rays  emitted  from  a  luminous 
point  and  reflected  from  a  mirror,  a  few  enter  the  eye  and 
form  a  virtual  image  of  the  point.  The  image  is  called  vir- 
tual, because  the  image  has  no  real  existence,  and  the  rays 
only  appear  to  come  from  the  other  side  of  the  mirror. 

Let  A  B  be  an  arrow  in  front  of  a  mir- 
ror, M  N.  The  image  of  the  point,  A, 
will  appear  to  come  from  A';  that  of  B, 
from  B',  and  those  of  intermediate  points 
on  the  arrow  between  A7  and  W.  Hence, 
if  an  object  be  placed  before  a  plane 
mirror,  the  image  will  be  formed  at  an 
equal  distance  behind  the  mirror,  of  the 
same  size  as  the  object,  and  equally  inclined 
FIG.  193.  to  the  mirror. 

459.  The  object  and  image  have  to  each  other  twice  the 
inclination  that  each  has  to  the  mirror.     Hence,  trees  ap- 
pear   inverted    by    reflection    from    a    tranquil    surface    of 
water. 


250 


NATURAL   PHILOSOPHY. 


If  the  mirror  and  object  are  parallel  to  each  other,  there  is  a  semi- 
inversion  in  one  dimension  only.  If  a  pri-son  stands  before  a  vertical 
mirror,  the  image  of  his  right  hand  will  be  on  the  left  side  of  his 
image.  So,  also,  if  a  printed  page  is  held  before  a  plane  mirror,  the 
letters  appear  reversed  in  a  horizontal  direction,  or  right  and  left. 
Since  the  angle  of  incidence  is  equal  to  the  angle  of  reflection,  a  person 
may  see  his  entire  image  in  a  vertical  mirror  of  half  his  length. 

460.  Multiple  images.  If  two  mirrors  are  at  right 
angles,  a  luminous  point  placed  between  them  will  give 
three  images.  If  the  mirrors  are  inclined  60°,  five  images 


FIG.  194. 


are  produced,  and  seven  if  the  angle  is  45°.  The  number 
of  images  increases  as  the  angle  diminishes,  and  would  be 
infinite  when  the  mirrors  are  parallel,  if  the  light  were  not 
gradually  weakened  at  each  successive  reflection. 

461.  The  kaleidoscope  is  an  optical  toy  which  illustrates 
this  property  of  inclined  mirrors.  It  consists  of  a  paper 
tube  containing  two  or  more  long  and  narrow  mirrors,  ni- 
di m-d  to  each  other;  one  end  of  the  tube  is  closed  by 
Around  L'luss  and  the  other  by  plain  glass.  Small  bits  of 
colored  glass  are  placed  in  a  cell  between  the  ground  irlass 
and  another  glass  disk,  leaving  just  room  enough  for  the 
objects  to  tumble  about  as  tin-  tube  is  turned.  On  looking 


CURVED  MIRRORS.  251 

through  the  tube,  the  objects  and  their  images  are  seen  in 
beautiful  forms. 

That  there  may  be  perfect  symmetry  in  these  forms,  the  angle  of 

the  mirror  must  be  an  aliquot  part  of  360°.     The  best  inclination  for 

two  mirrors  is  30°.     Three  mirrors  are  usually  employed,  furnishing 

three  angles  of  60°  each.     In  a  well  constructed  instrument,  an  end- 

iriety  of  beautiful  and  symmetrical  figures  may  be  obtained. 

462.  Curved  mirrors  may  be  considered  as  made  up  of 
an  infinite  number  of  plane  mirrors,  inclined  to  each  other. 
Each  ray  of  light   will  be  reflected 

exactly  as  if  it  fell  on  a  plane,  tan- 
gent at  the  point  of  incidence.  Let 
T  T'"  be  a  section  of  a  small  portion 
of  a  spherical  surface.  C  will  be  the 
center  of  curvature.  The  line,  C  V, 
which  passes  through  the  vertex  of 
the  mirror  is  called  the  principal  axis  FlQ.  195. 

of  the  mirror,   and    any  other  line, 

as  CC',  which  passes  through  the  center  of  curvature  is  called 
a  secondary  axis.  Any  radius,  as  C  I,  is  perpendicular  to  the 
concave  surface,  and  its  prolongation,  C'  I  is  perpendicular 
to  the  convex  surface. 

463.  Concave  spherical  mirrors.     If  a  luminous  point  be 
on  the  principal  axis,  the  image  formed  on  reflection  will 
vary  in   position  with  the  distance  of  the   point.     If  the 
point  is  at  an  infinite  distance,  the  rays  will  be  sensibly 
parallel  to  the  axis. 

M 

H 


FIG.  196. 


(1.)  In  Fig.  196,  the  radii,  C  M,  C  B,  CD,  are  perpendicular  to 
the  surface.  The  parallel  rays,  H  B,  G  D,  L  A,  will  each  be  reflected 
so  that  the  angle  of  incidence  for  each  ray  equals  the  angle  of  reflec- 


252 


NATURAL  PHILOSOPHY. 


tion,  and  hence  will  converge  after  reflection.  If  the  mirror  is  not 
more  than  10°  of  angular  aperture,  all  the  rays  will  meet  at  F,  very 
nearly  half-way  between  the  center  of  curvature  and  the  mirror. 
This  point  is  called  the  principal  focus  of  the  mirror. 

If  the  luminous  point  is  at  a  finite  distance,  the  rays  will 
be  divergent. 

(2.)  If  the  point  is  at  L,  beyond  the  center  of  curvature,  Fig.  197, 
the  rays  will  converge,  on  reflection,  to  a  point,  /,  between  the  center 
and  the  principal  focus.  (3.)  Conversely,  if  the  luminous  point  is 


FIG.  197. 

at  /,  rays  will  converge,  on  reflection,  to  the  point  L.  The  points,  L 
and  /,  are,  therefore,  called  conjugate  foci.  The  nearer  the  luminous 
point,  L,  is  to  the  center  of  curvature,  the  nearer  will  its  conjugate 
focus,  /,  approach  to  the  center. 

(4.)  If  the  luminous  point  be  at  the  center  of  curvature,  all  the  rays 
will  fall  perpendicularly  on  the  mirror,  and  will  be  reflected  back  to 
the  center.  In  all  these  cases  the  focus  is  real,  and  on  the  same  side 
of  the  mirror  as  the  object. 

(5.)  If  the  luminous  point  be  at 
the  principal  focus,  the  reflected  rays 
will  be  parallel,  and  there  will  be  no 
focus.  Fig.  196. 

(6.)  If  the  luminous  point  be  be- 
tween the  principal  focus  and  the 
mirror,  the  rays  will  diverge  as  it 
from  a  point,  /,  behind  the  mirror. 
Fig.  198.  This  point  is  called  the 

virtual  focux.  When  the  luminous  point  is  near  the  principal  focus, 
the  virtual  focus  will  heat  a  great  di-tance  In-hind  the  mirror;  hut 
as  the  luminous  point  approaches  the  mirror,  the  virtual  locus  also 
approach*-  it;  and  (7.)  when  the  luminous  point  is  at  tin-  surface, 
the  two  coincide. 

464.  Secondary   axes.     If  the  luminous   point   be  on  a 


Fio.  198. 


FORMATION  OF  IMAGES. 


253 


secondary  axis,  the  focus  of  any  point,  L,  will  be  found  on 
this  axis,  1>\  the  same  reason- 
ing as  in  the  preceding  cases. 
Fig.  199. 


465.  The  images  formed  by 
concave  mirrors  may  be  de- 
termined by  finding  the  foci 

„  '  f         -1  A  1  FlG-   199' 

for  a  series  of  points.     A  col- 
lection of  these  foci  will  constitute  an  image,  either  real  or 
virtual. 

The  real  image  will  be  formed  when  the  object  is  beyond 
the  principal  focus.  The  image  is  real,  for  it  may  be  re- 
ceived on  a  screen,  or  it  may  be  seen  by  placing  the  eye  in 
the  direction  of  the  reflected  rays. 

1.  If  the  object  is  at  an  infinite  distance,  no  image  will 
be  formed,  but  there  will  be  a  concentration  of  light  at  the 
focus. 

2.  Let  the  object  be  placed  at  a  finite  distance  beyond  the 
center  of  curvature,  as  AB,  Fig.  200.     From  the  point,  A, 
draw  the  secondary  axis,  A  E,  and  the  incident  rays,  A  D, 
AH.    Make  the  angle  of  reflection,  a  DC,  equal  to  the  angle 
of  incidence,  ADC.     The  point,  a,  where  the  reflected  ray 
cuts  the  secondary  axis,  is  the  conjugate  focus  of  the  point, 
A.     Similarly,  b  is  the  conjugate  focus  of  the  point,  B. 


FIG.  200. 


Between  these  two  extremes,  the  images  of  the  other  points 
of  the  object  will  be  found,  and  hence  a  b  is  the  complete 
image  of  A  B.  The  image  is  inverted,  smaller  than  the  object, 
and  placed  between  the  center  and  the  principal  focus. 


254  NATURAL  rniLosoniY. 

3.  The  image  increases  in  size  as  the  object  approaches 
the   principal   focus.     At  the   center,  the  ima.uv  is  inverted, 
of  the  same  size  as  the  object,  and  at  the  same  distance  from 
the  mirror. 

4.  If  the  object  is  between   the  center  and  the   principal 
focus,  as  at  a  b,  Fig.  200,  the  image  will  be  at  A  B  inverted, 
beyond  the  center,  and  enlarged.     The  nearer  the  object  is  to 
the  focus,  the  larger   will  be   the  image,  and  the  farther 
beyond  the  center. 

The  real  image  is  always  inverted,  and  recedes  from  the  mirror  as 
the  object  approaches  it,  and  vice  versa.  Reflecting  telescopes  give  a 
small  but  very  distinct  image  of  the  heavenly  bodies,  which  are 
viewed  after  being  enlarged  by  the  use  of  lenses.  Burning  mirrors 
are  concave  reflectors,  which  collect  the  parallel  rays  of  the  sun  at 
the  principal  focus.  The  light  and  heat  increase  in  intensity  as  the 
area  of  the  mirror  exceeds  the  area  of  the  focus. 

5.  No  image  is  formed  when  the  object  is  at  the  principal 
focus,  for  the  rays  are  reflected  parallel. 

This  principle  is  applied  in  light-houses.  The  light  is  placed  in 
the  focus  of  a  concave  mirror,  and  its  rays  are  reflected  in  parallel 
lines  from  every  point  of  the  mirror. 

466,  The  virtual  image  is  formed 
when  the  object  is  between  the  prin- 
cipal focus  and  the  mirror. 

6.  Let  A  B  be  an  object  between  the 
principal  focus  and  the  mirror.  Draw 
the  axes,  C  A,  C  B,  and  produce  them 
behind  the  the  mirror.  The  pencil  at  A 
will  be  reflected  to  the  eye  at  E,  appear- 
ing to  radiate  from  a,  in  the  same  axis ; 
likewise  those  from  B,  as  from  6. 

The  image  is  virtual  because  it  is 
behind  the  mirror,  erect,  as  the  rays 
do  not  cross  each  other,  ami  <  n- 
larged,  because  the  visual  angle  of  the  image  is  larger  than 
that  of  the  object. 

The  visual  angle  is  largest,  when   the  object  is  near  the 


CONVEX  MIRRORS. 


255 


focus.  As  the  object  approaches  the  mirror,  the  image 
becomes  smaller,  and  when  the  object  is  at  the  surface,  the 
image  is  of  the  same  size. 

467.  Convex  spherical  mirrors.  In  a  convex  mirror  all 
the  foci  are  virtual.  They  may  be  found  in  the  manner 
already  detailed  for  finding  the  foci  of  concave  mirrors. 

In  Fig.  202,  the  parallel  rays,  SI,  T  K,  take,  on  reflection,  the 
directions  I M,  K II,  which  appear  to  diverge  from  the  point,  F, 
which  is  the  principal  virtual  focus  of  the  mirror.  This  point  lies 
very  nearly  half-way  between  the  center  of  curvature  and  the  mirror. 


F;;:;-C 


FIG.  202. 

Kays  diverging  from  a  luminous  point,  as  L,  at  a  finite  distance 
from  the  mirror  will  form  a  virtual  focus,  I,  between  the  principal 
focus  and  the  mirror.  Diverging  rays  are  rendered  more  divergent 
by  reflection  from  a  convex  mirror. 

468.  Formation  of  images  in  convex  mirrors.  Let  AB, 
Fig.  203,  be  an  object  placed  at 
any  finite  distance.  The  pencil 
from  A  appears  to  radiate  from 
a,  in  the  same  axis,  A  C ;  that 
from  B,  as  if  from  b,  in  the 
axis,  B  C.  Therefore,  the  image 
formed  by  convex  mirrors  is 
always  virtual,  erect,  and  smaller 
than  the  object. 

469a.  In  all  cases  of  spherical 
mirrors  the  diameter  of  the  image 
varies  with  the  distance  of  the  ob- 
ject from  the  mirror ;  hence,  the  size  of  the  image  is  inde- 


M 


256  NATURAL   PHILOSOPHY. 

pendent  of  the  area  of  the  mirror.  An  increase  in  the  area 
of  the  mirror  increases  the  briyhtncts  of  the  image,  by  inter- 
cepting more  of  the  luminous  rays  proceeding  from  the  object. 

469b.  Spherical  aberration.  The  laws  already  de- 
duced for  the  formation  of  foci  and 
images  from  spherical  mirrors, 
are  not  strictly  accurate  unless  the 
mirror  is  a  very  small  portion  of 
a  spherical  surface.  If  the  aper- 
ture of  the  mirror  exceeds  10°, 
the  rays  reflected  from  the  borders 
of  the  mirror  meet  the  axis  nearer 
FIG.  204.  the  mirror  than  those  which  are 

reflected    from    points    nearer  the 

vertex.  The  effect  of  this  is  to  render  the  image  indistinct 
or  less  sharply  defined.  This  defect  is  termed  spin-rind 
<il><  I- rut  Ion  by  reflection.  Every  pair  of  reflected  rays  succes- 
sively intersect  each  other,  and  their  foci  form  a  curved  line, 
called  a  caustic  by  reflection.  Fig.  204.  Thus,  the  heart-shaped 
curve,  formed  by  the  reflection  of  a  lighted  candle  from  the 
concave  surface  of  a  tumbler  containing  milk,  is  a  caustic. 

Surfaces  generated  by  the  revolution  of  parabolas  about 
their  axes,  reflect  without  aberration.  Hence,  parabolic 
mirrors  are  used  for  the  lanterns  of  locomotives,  because, 
if  a  luminous  point  be  placed  in  the  focus  of  a  concave 
parabolic  mirror,  all  the  rays  which  fall  on  the  mirror 
will  be  reflected  exactly  parallel.  The  light  thus  reflected 
maintains  its  intensity  for  a  great  distance. 

470.  Recapitulation. 
The  intensity  of  light  varies: 

I.  When  emitted  by  luminous  bodies: 

1.  With  the  source. 

2.  Inversely  as  the  square  of  the  distance. 

II.  When   rel!ert»-(l   from  non-luminous  lto<li< 

3.  With  the  nature  of  the  surface. 


DIOPTRICS. 


257 


4.  With  the  polish  of  the  surface. 

5.  With  the  angle  of  incidence. 

Mirrors  are  either  plane  or  curved. 

r Convex. 
f  Spherical  {ConcaTe. 

Curved  mirrors  are (.Conical      /  Pa™bol°id- 

\  Ellipsoidal,  etc. 

REFRACTION    OF    LIGHT,    OR   DIOPTRICS. 

471.  When  a  pencil  of  light  falls  on  a  transparent  body, 
(1.)  some  of  the  rays  are  reflected,  (2.)  some  are  absorbed, 
and  (3.)  the  rest  of  the  rays  are  transmitted.  When  a  ray 
of  light  passes  obliquely  from  one  medium  to  another,  it  un- 
dergoes a  change  of  direction,  which  is  called  refraction. 

The  actual  occurrence  of  this  change  in  direction  may  be  shown 
by  placing  a  coin  in  an 
empty  cup,  in  such  a  posi- 
tion that  it  is  just  out  of 
sight;  if,  now,  the  cup  be 
gently  filled  with  water, 
the  coin  will  appear  to  be 
elevated  and  will  become 
visible,  although  neither 
the  eye  nor  the  coin  has 
changed  its  position.  Thus, 
if  A  B  be  the  surface  of  the 
water,  the  ray,  raE,  proceed- 
ing from  the  coin,  will  be  so  refracted  when  it  passes  from  the  water 
into  the  air  as  to  appear  to  come  to  the  eye  in  the  line  m'l  E. 

472.  Suppose  an  incident  ray 
of  light,  A  C,  moving  in  air,  to 
meet  the  surface  of  water,  R  S, 
and  let  C  E  be  the  refracted  ray. 
Draw  P  C  F  perpendicular  to  the 
surface  at  the  point  of  incidence, 
C ;  thus,  A  C  P  is  the  angle  of  in- 
cidence, and  the  angle,  ECF,  lying 
between  the  perpendicular  and  the 
refracted  ray  is  called  the  angle  of  refraction.  If,  now,  we 

N.  P.  17. 


FIG.  205. 


FIG.  2i)6. 


258  NATURAL   PHILOSOPHY. 

make  the  distances,  AC  and  CE  each  equal  to  some  unit 
of  length,  and  draw  A  D,  E  F  each  perpendicular  to  P  F, 
the  line,  A  D,  is  the  sine  of  the  angle  of  incidence,  and  the 
line,  E  F,  the  sine  of  the  angle  of  refraction.  If  the  incident 
ray  falls  more  obliquely,  as  at  a  C,  the  sine  of  the  angle 
of  incidence,  a  d,  becomes  larger,  and  the  sine  of  the  angle 
of  refraction,  ef,  increases  in  the  same  proportion,  so  that 
the  ratio  between  the  sines  of  the  angles  of  incidence  and 
refraction  is  constant  for  the  same  two  media.  This  ratio 
is  called  the  index  of  refraction,  and  may  be  obtained  by 
dividing  A  D  by  E  F. 

473.  The  index  of  refraction  varies  with  the  media : 
thus,  if  light  passes  from  air  into  water,  the  index  of 
refraction  is  about  J,  from  air  into  glass,  about  f .  The 
reciprocals  of  these  numbers  will  give  the  indices  of  refrac- 
tion when  light  passes  in  the  opposite  direction  ;  thus,  from 
water  to  air  it  is  J,  and  from  glass  to  air  -f. 

The  following  table  gives  the  indices  of  refraction  when  light 
pa-fs  from  a  vacuum  into  any  of  the  substances  named.  The  index 
of  refraction  for  any  two  substances  may  be  found  by  dividing  the 
absolute  index  of  one  by  that  of  the  other. 

Table  of  Absolute  Indices  of  'Refraction. 


Vacuum 1.00000 

Air  1.00029 

Carbonic  acid 1.00045  I  Oil  of  cassia 1.641 

Ice 1.309 

W.-.trr 1.336 

Alcohol 1.374 

Alum 1.4-->7 


Crown  glass 1.534 

Quartz  crystal 1.548 


Bisulphide  of  carbon 1.76S 

Flint  glass 1.830 

Diamond 2.4.".!» 

Chromate  of  lend...  ..  2.974 


474.  The  direction  of  refraction  depends  on  the  relative 
velocity  of  lijrht  in  the  two  media.  The  velocity  of  light  is 
least  in  the  more  hiirhlv  refractive  media. 

The  refractive  power  increases,  in  ^i-m-i-al.  with  the  spe- 
cific gravity  of  the  -ul.-tance  ;  lmt  inflammable  bodies,  like 
alcohol  and  the  essential  oils,  have  a  irn-at-T  refractive 
power  than  water,  although  their  specific  gravity  is  less. 


A  TMOSPHERIC  REFRA  CTION. 


259 


In  optic?,  the  word  dense  is  used  to  signify  of  great  refract- 
ive power,  and  rare,  of  little  refractive  power,  without 
reference  to  specific  gravity;  in  this  sense  water  is  rarer 
than  alcohol. 

Laws  of  refracted  light.     1.    When  light  passes  perpendic- 
itlnrhj  from  one  medium  to  another,  it  is  not  refracted. 

2.  When  lifjht  passes  obliquely  from  a  rarer  to  a  denser  me- 
dium, it  is  refracted  toward  the  perpendicular. 

3.  When  light  passes  obliquely  from  a  denser  to  a  rarer  me- 
dium, ii  is  refracted  from  the  perpendicular. 

475.  Total  reflection.     As  a  consequence  of  the  third  law, 
when  light  passes  from  a  denser  to   a  rarer  medium,  the 
angle  of  refraction  is  always  greater  than  the  angle  of  inci- 
dence. 

Thus,  if  light  passes  from  water  into  air,  as  the  angle  of  the  inci- 
dent ray,  I.  V,  I",  increases,  the  angle  of  the  refracted  ray,  R,  R1, 
R2,  also  increases.  There  will  be 
found  some  ray,  as  L,  where  the 
angle  of  refraction  is  a  right  angle, 
and  the  ray,  if  refracted,  would  co- 
incide with  the  surface  OB.  But 
if  the  incident  angle  exceeds  this 
limit,  as  T,  the  ray  can  not  pass  into 
the  air,  but  will  be  totally  reflected  to  T'. 
The  limiting  angle  varies  inversely 
as  the  refractive  power:  for  water, 
it  is  48°  28',  for  crown  glass,  40°  49', 
for  diamond  24°  12'. 

This  result  may  be  shown  by  fill- 
ing a  glass  with  water  and  placing 

in  it  a  silver  spoon.  An  eye,  placed  a  little  below  the  level  of  the 
water,  may  see  a  bright  image  of  the  part  of  the  spoon  immersed, 
reflected  from  the  surface  of  the  water. 

476.  Atmospheric  refraction  causes  the  heavenly  bodies 
to  appear  higher  than  they  really  are,  except  when  in  the 
zenith.     The  nearer  the  sun  or  a  star  is  to  the  horizon,  the 
greater  will  be  the  effect  of  the  refraction  in  increasing  its 
altitude.     The  sun   and  stars   are  visible,  even  when  they 


FIG.  207. 


260  NATURAL    PHILOSOPHY. 

are  below  the  horizon.  The  refractive  power  of  a  gas  in- 
creases witli  its  density,  and,  as  the  successive  strata  of  the 
atmosphere  are  denser  as  they  approach  the  earth,  the  rays 
from  a  luminary  near  or  below  the  horizon  are  refracted 
more  and  more,  describing  a  curve,  and  appearing  to  the 
eye  to  be  in  the  direction  of  a  tangent  to  this  curve.  Twi- 
light is  due  to  the  successive  refractions  and  reflections  of 
the  sun's  rays  when  it  is  below  the  horizon. 

477.  When  the  density  of  the  atmosphere  varies  from 
its  ordinary  state,  the  unusual  refraction  thus  arising  pro- 
duces various  phenomena.  Distant  objects,  not  usually 
visible,  sometimes  appear  to  be  near  and  elevated  in  the  air. 
The  looming  of  objects  at  sea  is  due  to  an  increase  in  the 
density  of  the  strata  near  the  earth's  surface. 

The  mirage  of  the  desert  results  from  a  decrease  in 
the  density  of  the  strata  of  the  air  caused  by  contact  with 


FIG.  208. 

the   heated    -oil.      Kays   from    an    elevated   object,  M,  Fig. 

208,  are  transmitted  through  strata  \vhich  grow  less  refract- 

Mid.    ultimately,    the   incident    ray  reaches  the   limiting 

and    i-    totally   reflected.      The   ray  then    rises,    and    is 

refracted  in  a  direction  contrary  to  the  (ir>t,  until   it  reaehes 

the  eye  in  the  same  direction  as  if  it    had   proceeded  from  a 


REFRACTION  BY  PARALLEL    PLANES.  261 

point  below  the  ground.  Hence  it  gives  an  inverted  image 
of  the  object,  just  as  if  it  had  been  reflected  at  A,  from 
the  surface  of  a  tranquil  lake.  This  illusion  often  deludes 
the  traveler  in  arid  regions  with  the  hope  of  finding  water; 
but  as  he  approaches  it  recedes,  until,  at  last,  the  real  ob- 
jects are  seen  by  means  of  direct  light. 

The  inverted  images  of  very  distant  ships  are  frequently 
seen  at  sea.  This  form  of  mirage  is  the  reverse  of  the  pre- 
ceding, because  the  lower  strata  of  the  atmosphere  are  ren- 
dered colder  and  denser  than  those  above  by  contact  with 
the  water.  Sometimes  this  phenomenon  is  combined  with 
extraordinary  looming,  so  that  an  erect  image  is  observed 
in  the  air  above  an  inverted  image,  when  the  ship  is  really 
below  the  horizon. 

478.  Refraction  by  regular  surfaces.  If  a  transparent 
medium  is  denser  than  the  air,  and  is  entirely  surrounded 
by  air,  a  ray  of  light,  on  entering  the  medium,  will  be 
refracted  toward  the  perpendicular,  and,  on  emerging  from 
the  medium,  will  be  refracted  from  the  perpendicular.  The 
relative  direction  of  the  incident  and  emergent  rays,  will 
depend  on  the  inclination  of  the  two  faces  of  the  medium. 

1.  Parallel  planes.     When  a  ray  of  light  is  transmitted 
through  a  medium,  bounded  by  plane  and  parallel  surfaces, 
the  incident  and  emergent 
rays    are   parallel,   because 
the  ray  is  refracted  an  equal 
amount  at  each  surface,  but 
in     a     contrary    direction. 
The  two  refractions  do  not 
produce    a    change    in    the 
general  direction  of  the  ray, 
but   simply  produce   a   lat- 
eral aberration,  whose  amount  increases  with  the  thickness 
of  the  medium,  and  the  obliquity  of  the  incident  rays. 

A  pane  of  glas.s,  whose  sides  are  perfectly  parallel,  occasions  no 
distortion  of  objects  seen  through  it;  if,  however,  the  sides  are  not 


262 


NA  T  URA  L   PHIL  OS  OF  in '. 


P", 


FIG.  210. 


parallel,  the  objects  seen  through  the  glass  are  distorted  in  proportion 
to  the  inequality  in  the  thickness  of  the  glass. 

2.  A  prism  is  a  transparent 
medium,  having  two  plane  sur- 
faces, not  parallel.  The  prism 
may  be  a  solid  wedge  of  glass, 
ice,  or  crystal,  or  may  consist  of 
liquids  inclosed  in  hollow  prisms 
with  sides  of  plane  glass. 

Let  A  C  B  be  the  section  of  a  prism,  and  O  a  luminous  point. 
The  incident  ray,  O  D,  on  entering  the  prism  is  refracted  toward  the 
perpendicular,  P  P',  because  it  enters  a  denser  medium,  and  will 
proceed  in  the  line,  D  K.  On  leaving  the  prism  for  a  rarer  medium, 
it  will  be  refracted  from  the  perpendicular,  P'  P",  and  will  emerge 
in  the  direction,  KH.  The  light  is  thus  twice  refracted  toward  the 
base  of  the  pi*ism,  and  the  eye  which  receives  the  emergent  ray,  K  H, 
sees  the  object  at  O'  nearer  the  summit  of  the  prism  than  the  real 
position  of  the  point,  O. 

3.  A  lens  is  a  transparent  medium  having  two  curved 
surfaces,  or  one  curved  and  one  plane  surface.  Lenses  are 
usually  made  of  crown  or  of  flint  glass  with  spherical  sur- 
faces. There  are  six  varieties  of  spherical  lenses,  viz.:  A 
is  a  double  convex,  B  is  a  plano-convex,  C  is  a  meniscus,  con- 


/ 


Fio.  211. 


vex  on  one  side  and  concave  on  the  other,  the  convex  sur- 
face having  the  >hortcr  radius.  D  is  a  Jmible  concave,  K  is 
a  plano-concave,  and  F  is  a  concavo-convex,  the  concave  sur- 
face ha v in ir  the  shorter  radius. 

479.  Lenses  arc   divided   into   two  groups,  the  first  three 
are  converyiny,  and  are  thickest  at  the  center;   the  others  are 


FOCI   OF  LENSES.  263 

diverging,  and  are  thinner  at  the  center  than  at  the  edges. 
The  double  convex  lens  will  be  taken  as  the  type  of  the 
first  group,  and  the  double  concave  lens  as  the  type  of  the 
second,  as  the  properties  of  these  lenses  will  represent  those 
of  the  others. 

The  right  line,  MX,  which  passes  through  a  lens  perpendicular 
to  both  surfaces  is  called  the  axis  of  the  lens.  The  centers  of  curvature 
are  the  centers  of  the  spherical  surfaces.  The  double  convex  lens 
may  be  regarded  as  a  series  of  prisms,  whose  bases  are  turned  toward 
the  axis,  and  the  double  concave  lens  as  a  series  of  prisms,  whose 
bases  are  turned  away  from  the  axis.  If  the  sides  of  each  prism  are 
infinitely  small,  the  series  will  form  a  spherical  surface.  The  per- 
pendiculars drawn  to  the  points  of  incidence  and  of  emergence  will, 
evidently,  correspond  to  the  radii  of  the  spherical  surfaces.  Hence, 
as  a  prism  refracts  light  toward  its  base,  a  convex  lens  will  refract 
light  toward  its  axis,  or  tend  to  converge  the  rays ;  and  a  concave  lens 
will  refract  light  away  from  the  axis,  or  tend  to  disperse  the  rays. 

480.  The  principal  focus  of  a  convex  lens,  'is  the  point 
at  which  parallel  rays  unite  after  refraction.     Any  incident 
ray,  as  L  B,  will  be  twice  refracted  toward  the  axis,  which 
it  cuts  in  F.     This  focus 

is  real,   for  the   rays   of 
the  sun  may  all  be  col- 
lected at  this  point.    The   M 
ordinary    burning    glass 
is  simply  a  large  double 
convex    lens.     The    dis- 
tance   of  the  point,    F,  FIG.  212. 
from   the  center   of  the 

lens,  is  called  the  principal  focal  distance.  This  varies  with 
the  radii  of  curvature,  and  also  with  the  index  of  refraction. 
In  a  double  convex  lens  of  crown  glass,  it  is  equal  to  the 
radius  of  curvature,  and  in  a  plano-convex  glass  it  is  equal 
to  twice  the  radius.  The  greater  the  refracting  power  of  the 
substance,  the  nearer  will  the  principal  focus  be  to  the  lens. 

481.  Real  conjugate  foci  are  formed  when  a  near  object 
is  beyond  the  principal  focus.     Thus,  if  a  luminous  point 


264 


NATURAL   PHILOSOPHY. 


be  at  L,  Fig.  213,  the  diverging  rays  will  converge  on  re- 
fraction to  I,  and,  conversely,  rays  from  /  will  converge  on 
refraction  at  L.  If  a  luminous  point  be  placed  at  the 
DAB  11 


FIG.  213. 


principal  focus,  Fig.  212,  the  emergent  rays  will  be  parallel. 
A  lamp  so  placed  will  illuminate  objects  at  great  distances. 

482.  A  virtual  focus  is  formed  when  the  luminous  point 
is  between  the  lens  and  the  principal  focus.  Thus,  rays 
diverging  from  L,  will  be  rendered  less  divergent  on  refrac- 


FlG.  214. 

tion,  and  will  appear  to  come  from  the  point  I  on  the  axis. 

Thus,  the  virtual    focus  is   on   the   same  side  of  the  lens  as 

the  object;  the  real  foci  are  on  the  opposite  side. 
483.  Secondary   axes.      If  two   radii,   CA,    C'A',   Fig. 

215,  an-  drawn  parallel  to  each  other,  their  tangents  will 
also  be  parallel.  Hence,  a  ray  of  light 
which  reaches  A  at  such  an  anirle  that 
after  refraction  it  takes  the  direction, 
A  A',  will  emerge  from  A'  as  if  trans- 
mitted through  a  medium  with  parallel 
faces.  Therefore,  the  emeip-nt  ray, 
K'  A',  will  he  parallel  to  the  incident 
ray,  K  A.  The  lateral  aberration 

caused  by  the  slight  thickness  of  the  lens  may  be  neglected, 


FORMATION   OF  IMAGES. 


265 


and  the  incident  ray  considered  as  in  the  same  straight  line 
with  the  emergent  ray.  The  point,  O,  where  the  line,  A  A', 
cuts  the  principal  axis,  is  called  the  optical  center  of  the 
k-ns.  Any  right  line  which  passes  through  the  optical 
center  without  passing  through  the  centers  of  curvature,  is 
a  secondary  axis.  A  luminous  ray,  coinciding  with  a  sec- 
ondary axis,  suffers  no  deviation  in  direction. 

So  long  as  secondary  axes  are  nearly  parallel  with  the  principal 
axis,  foci  may  be  formed  on  them  in  the  same  manner  as  on  the 
principal  axis.  A  collection  of  these  foci  will  determine  the  position 
of  images  formed  by  lenses. 

484.  Formation  of  images  by  convex  lenses.  Real 
images  are  formed  when  the  object  is  at  a  finite  distance 


FIG.  216. 

beyond  the  principal  focus.  Let  A  B  be  an  object  so  placed. 
Draw  a  secondary  axis,  A  a,  from  the  top  of  the  object  A. 
Any  other  ray  diverging  from  A,  as  A  C  or  A  E,  after  being 
twice  refracted  will  cut  the  secondary  axis  at  a.  This  point 
is  the  conjugate  focus  of  A.  In  the  same  manner,  the  con- 
jugate focus  of  B  will  be  found  at  b,  and  intermediate 
points  on  the  object  will  have  their  foci  between  a  and  b. 
Hence,  a  real  and  inverted  image  of  A  B  will  be  found  at 
a  b.  Reciprocally,  if  a  b  were  a  luminous  object,  its  image 
would  be  formed  at  A  B.  Hence, 

1.  If  an  object  be  placed  more  than  twice  the  principal 
focal  distance  from  a  double  convex  lens,  the  image  will  be 
smaller  than  the  object,  real,  and  inverted. 

2.  If  a  small  object  be  placed  less  than  twice  the  princi- 
pal focal  distance,  but  beyond  the  focus,  the  image  will  be 
larger  than   the  object,  real,  and  inverted.     In   both   cases, 


266 


NATURAL    PHILOSOPHY. 


the  diameter  of  the  object  is  to  that  of  its  image  as  the 
distance  of  the  object  is  to  the  distance  of  the  image  from 
the  lens.  These  principles  can  be  verified  by  placing  a 
candle  at  different  distances  from  a  double  convex  lens, 
and  receiving  its  image  on  a  sheet  of  white  paper. 

485.  Virtual  images  are  formed  when  the  object  is  placed 
between  the  lens  and  the  principal  focus.  In  Fig.  217, 
draw  the  secondary  axis,  O  a,  through  the  point  A.  Every 
ray,  as  A  C,  after  twp  refractions,  appears  to  emerge  diver- 


Fia.  217. 

gent  from  this  axis.  The  point,  a,  where  the  emergent  ray, 
continued  backward,  cuts  the  secondary  axis,  is  the  virtual 
focus  of  A.  The  virtual  focus  of  the  point  B,  is  at  b. 
There  is,  therefore  an  image  of  A  B  at  ab,  virtual,  erect, 
and  larger  than  the  object. 

In  thi>  <-a-c,  the  lens  is  a  simple  magnifying  glass.  The  size  of  the 
image  is  independent  of  the  area  of  the  lens,  but  is  greater  as  the 
lens  is  more  convex,  and  the  object  nearer  the  principal  focus.  The 
iniML'f  i-  liri'iliffi-  ;i-  the  area,  or  field  of  view  increases,  because  more 
rays  tVoin  the  object  enter  the  lens. 

486.  The  foci  of  concave  lenses  arc  always  virtual.     Let 
L,  Fig.  218,  be  a  luminous  point. 
The  incident  ray,  LI,  will  be  re- 
fracted  at  I,  toward   the  per  pen-  L 
dirtilar,  ('I,  and,  on  emerging,  it 
is  refracted   from  the  perpendicu- 
lar, G  C',  so   that  it  is  twice  re- 
IVactcd   away  from    the   axis,    L  C'. 
A-  this  is  the  case  with  every  ray,  the  emerging  rays,  G  K, 


CONCAVE  LENSES. 


267 


FIG.  219. 


M  N,  will  appear  to  diverge  from  a  virtual  focus,  I,  which 
is  between  the  principal  focus  and  the  lens. 

487.  The  images  formed  by  concave   lenses  are  always 
virtual.     Let  AB  be  an  object  in  front  of  a  double  con- 
cave lens.     Draw  the  sec- 
ondary axis,    A  O.      Each 

ray  from  the  point,  A,  as 
A  I,  AC,  is  twice  re- 
fracted, diverging  from  the 
axis,  so  that  the  eye,  placed 
in  the  direction  of  the 
emergent  rays  D  E  and 
G  H,  receives  them  as 
if  coming  from  the  point 

a,  where  their  prolongations  cut  the  secondary  axis.  The 
rays  from  B  appear  to  diverge  on  emerging  from  b.  There- 
fore, the  eye  sees  at  a  b  an  image  of  A  B,  which  is  always 
virtual,  erect,  and  smaller  than  the  object. 

488.  Spherical  aberration  by  refraction  is   due   to   the 
fact    that    the    rays    refracted    near    the    edge    of  the   lens 
meet  the  axis  a  little  nearer  the  lens  than   the  focus  of 
the  rays  passing  through   ,he  center.     The  effect  of  spher- 
ical aberration  is  to  render  the  image  less  distinct  and  well 
defined,  and  is  a  serious  defect  in  the  lenses  used  in  pho- 
tography.    If  the  angular  aperture,  which  is  obtained  by 
drawing  lines  from  the  principal  focus  to  the  edges  of  the 
lens,  does  not  exceed  10°,  the  defect  is  not  usually  regarded. 
It  may,  therefore,  be  partially  obviated  by  placing  before 
the  lens   a   diaphragm  which   cuts   off  the   rays  from   the 
edges,   and  may  be  entirely  destroyed  by  combining  two 
lenses  of  suitable  curvatures. 

• 

489.  Recapitulation. 

Light  is  not  refracted 

1.  In  passing  through  a  uniform  medium,  nor 

2.  When  passing  perpendicularly  from  one  medium  to  another. 


268  NATURAL   PHILOSOPHY. 

Light  is  refracted  in  passing  obliquely  into  a  second  medium, 

1.  Toward  the  perpendicular,  when  the  second  is  the  denser; 

2.  From  the  perpendicular,  when  the  second  is  the  rarer. 

{Double  convex. 
I'hiiio-convex. 

Lenses  are i  Meniscus. 

{Double  concave. 
Plano-concave. 
Concavo-convex. 

The  effects  of  concave  mirrors  and  convex  lenses  are  analogous ; 
that  is,  when  the  object  is 

1.  Nearer  than  the  principal  focal  distance, 
The  image  is  virtual,  erect,  and  magnified. 

2.  At  the  principal  focus, 

There  is  dispersion  of  light  in  parallel  rays. 

3.  Beyond  the  principal  focus,  but  less  than  twice  its  distance, 
The  image  is  real,  inverted,  and  magnified. 

4.  At  twice  the  principal  focal  distance, 

The  image  is  real,  inverted,  and  of  equal  size. 

5.  At  more  than  twice  the  principal  focal  distance,  but  finite, 
The  image  is  real,  inverted,  and  diminished. 

6.  At  an  infinite  distance 

There  is  concentration  of  light  at  the  principal  focus. 

The  effect  of  convex  mirrors  and  of  concave  lenses  are  also 
analogous,  forming  images  which  are  always  virtual,  erect,  and 
smaller  than  the  object. 

CHROMATICS,    OR   COLORS. 

490.  Decomposition  of  light.  If  a  pencil  of  solar  light 
be  admitted  into  a  darkened  room  through  a  very  small 
aperture,  it  will  form  a  round,  white  image  of  the  sun,  as 
represented  at  K,  Fig.  220.  If,  now,  a  prism  be  placed 
in -ar  the  aperture  in  the  path  of  the  pencil*  the  rays  will 
be  unequally  refracted,  and  will  form  on  a  screen  an  elon- 
gated, colored  image,  which  is  called  the  solar  spectrum. 
\-  «  ach  ray  forms  an  imairt'  of  the  sun,  the  sju-ctrum  may 
be  considered  as  an  infinite  number  of  colored  images, 


CHROMATICS. 


269 


overlapping  each  other  from  end  to  end.  If  any  ray  of  the 
>jHvtrum  be  transmitted  through  a  small  aperture  in  the 
screen,  and  received  on  another  prism,  it  will  again  be 


refracted,  but  will  undergo  no  further  change  in  color. 
Hence  all  the  prismatic  colors  are  simple.  Newton  dis- 
tinguished seven  of  these  colors  as  primary,  which  are  in 
order,  beginning  with  the  least  refracted,  red,  orange,  yellow, 
green,  blue,  indigo,  mold. 

491.  White  solar  light  is  therefore  composed  of  different 
colored  rays.     An  additional  proof  of  this  is  found  in  the 
fact  that,  when  all   the  colors  of  the   spectrum  are  recom- 
bined,  they  will  reproduce  white  light. 

Thus,  if  all  the  rays  of  the  spectrum  are  received  on  a  convex 
lens,  or  on  a  concave  mirror,  a  white  image  of  the  sun  will  be 
formed  in  the  focus.  If  a  circular  card  be  painted  with  the  seven 
colors,  in  sectors  proportional  in  extent  to  the  spaces  occupied  by 
these  colors  in  the  spectrum,  then  on  revolving  the  card  very  rapidly 
it  will  appear  of  a  white  color,  more  or  less  pure  according  as  the 
colors  on  the  card  more  or  less  exactly  imitate  those  of  the  spec- 
trum. Fig.  221. 

492.  Complementary   colors   are  any  two   colors   which 
combined  will  produce  white.     If  the  red  rays  of  the  spec- 
trum  are   intercepted,  and   the   remaining  colors  are   com- 
bined by  means  of  a  convex  lens,  the  resulting  image  will 


270 


NATURAL    PHILOSOPHY. 


be  green.  Hence,  green  and  red  are  complementary,  be- 
cause the  two  combined  contain  all  the  rays  of  white  light. 
In  this  manner  it  is  found  that  blue  and  orange,  violet  and 
yellowish  green,  indigo  and  orange  yellow  are  complement- 
ary colors. 


FIG.  221. 


Complementary  colors  may  be  seen  by  gazing  intently  at  any  blight 
colored  object  for  a  few  minutes,  and  then  turning  the  eye  toward  a 
white  wall.  Thus,  if  the  object  be  a  bright  red  wafer,  placed  oil  a 
sheet  of  black  paper,  the  eye,  on  turning  away,  will  retain  *fl  impres- 
sion of  the  wafer,  in  its  complementary  color,  green.  If  tin  obj.-ri 
is  bright,  the  eye  will  sec  a  ring  of  a  color  complementary  to  that 
of  the  object  before  it  is  turned  away;  hence,  a  color  tetwfs  to  pfoduce 
in  the  eye  its  complement. 

493.  When  two  colors  are  placed  near  «ftch  other,  each 
color  will  1x3  modified,  as  though  mixed  With  th«  comple- 
ment of  the  adjacent  color. 

If  a  red  wafer  In-  placed  Wide  a  green  wafer,  each  color  will  be 
heightened,  liccnii-.-  the  red  wafer  will  tefld  to  tinge  the  adjacent 
nl.ject  gm-n,  <>r  to  make  it  greener;  and  thf»  given  wafer  will,  in  the 
same  manner,  tinge  the  red  with  red.  I/  it  be  desired  t«>  heighten 
a  color,  it  should  l»c  placed  l,(-ide  it>  complement,  but  if  it  be  de- 


FRAUNIIOFEffS  LINES. 


271 


sired  to  weaken  its  effect,  it  should  be  contrasted  with  others.  Thus, 
a  green  dress  or  scarf  increases  the  freshness  of  a  rosy  complexion. 
Florid  complexions  will  bear  dark  hues  in  dress,  but  a  pale  face 
appears  still  paler  when  a  black  dress  is  worn.  A  yellow  shawl  and 
an  orange  dress,  when  worn  together,  appear  mutually  dull,  but  the 
contrast  of  either  with  an  appropriate  shade  of  violet  would  be 
pleasant  and  tasteful. 

494.  Fraunhofer's  lines.  If  light  be  admitted  through 
a  very  narrow  slit  and  received  on  a  good  flint  glass  prism, 
it  will  be  found  not  only  that  the  colors  of  the  spectrum 


M 


DARK  H£  AT  RAYS 


W,      x, 

*   1 


I  JJJ  J 

2  S      I  CHEMICAL 


FIG.  222. 


are  not  continuous,  but  also  that  they  are  interrupted  by 
numerous  dark  spaces,  known  as  Fraunhofer's  lines.  On 
viewing  the  spectrum  with  a  powerful  telescope,  two 
thousand  of  these  lines  are  visible.  Seven  of  these  are 
more  distinct  than  the  rest,  and  are  designated  by  the 
letters,  B,  C,  D,  E,  F,  G,  H,  to  serve  as  means  of  refer- 
ence. The  positions  of  these  lines  in  the  spectrum,  due  to 
solar  light,  direct  or  reflected  from  the  moon  and  planets, 
is  invariable,  but  their  distances  from  each  other  vary  with 
the  material  of  the  prism.  Each  fixed  star  has  a  stellar 
spectrum,  which  differs  from  that  of  the  sun  and  other  fixed 
stars,  in  regard  to  the  number  and  position  of  the  dark 
lines. 

495.  Dispersion  of  light.  The  index  of  refraction  for 
the  different  colors  is  fixed  with  precision  by  ascertaining 
the  refraction  of  Fraunhofer's  lines,  B,  C,  etc.  The  table 
on  page  258  gives  the  indices  of  refraction  for  the  line,  E, 
in  the  yellowish-green  rays,  which  is  taken  as  the  mean  of 


272  NATURAL   PHILOSOPHY. 

all  the  rays.  If  similar  prisms  are  made  of  different  sub- 
stances, the  mean  refraction  may  be  nearly  the  same,  and 
yet  the  spectra  they  furnish  be  of  very  unequal  lengths. 
The  dispersive  power  of  a  medium  indicates  the  amount  of 
separation  which  it  produces  in  the  extreme  rays,  compared 
with  the  amount  of  refraction  in  the  mean  rays.  Thus, 
the  refractive  power  of  flint  glass  is  but  little  greater  than 
that  of  crown  glass,  but  its  dispersive  power  is  almost 
double. 

Table  of  Dispersive  ^Powers. 


Oil  of  cassia 0.139 

Bisulphide  of  carbon 0.130 

Flint  glass 0.052 

Diamond 0.038 


Green  crown  glass 0.036 

Water 0.035 

Alcohol  0.029 

Quartz  crystal 0.026 


496.  Chromatic   aberration,      As  lenses   are   merely    a 
series  of  prisms,  with   infinitely  small  faces,   they  disperse 

light  like  a  prism.  The  violet 
rays,  being  most  refracted,  come 
to  a  focus,  v,  Fig.  223,  nearest 
the  lens,  then  the  other  colors  in 
order,  the  red  being  the  most  re- 
no.  223.  mote.  Hence,  if  a  screen  be 
placed  a  little  nearer  the  lens 

than  the  focus  of  the  mean  rays,  the  image  will  be  fringed 
with  red.  If  the  screen  is  beyond  the  focus,  the  image  will 
be  fringed  with  violet,  because  the  violet  rays  cross  after 
coming  to  their  focus,  and  form  the  outside  of  the  diverging 
pencil.  The  difference  between  the  focal  distance  of  the 
red  and  violet  rays  causes  what  is  called  the  chromatic  aber- 
rnt'iun  of  the  lens.  The  chromatic  aberration  of  a  quartz 
Jen-  i-  small,  l>y  reason  of  its  low  dispersive  power. 

497.  Achromatism.      If  two   prisms,   exactly   alike,   are 
placed  near  cadi  other,  with  their  bases  turned  in  a  contrary 
direction,    one    will    exactly    neut rali/e    the    other,    and    the 
light  will    emerLT'1    from    the    second    a.-    if    from    a    medium 


ACHROMATISM. 


273 


with   parallel  faces.     If,   however,    the  first  prism,  B  C  F, 
be  of  crown  glass,  and  the  other  of  flint  glass,  the  disper- 
sion  may   be   destroyed   without  entirely   neutralizing  the 
refraction.       Since     the     dispersive 
power  of  flint  glass  is  almost  twice 
that  of  crown  glass,  the  refracting 
angle   of  the  former  must  be  made 
so    much    smaller   than    the    latter,      ^ 
that  the  dispersion  of  the  two  prisms 
shall  be  equal.     The  flint  glass  will 
then  entirely  neutralize   the   disper- 
sion  of  the  crown  glass,  but  will  destroy  only  about  half 
of  its  refractive  power. 

On  the  same  principle,  an  achromatic  lens  may  be  made 
by  combining  a  double  convex  lens  of  crown  glass  with  a 
concavo-convex   lens  of  flint  glass.      The   two 
lenses   must    have   such    curvatures    that    their      AlHillvB 
focal  lengths  shall  be  as  their  dispersive  powers. 
An    achromatic    lens    is,    therefore,    free    from 
chromatic  aberration. 

498.  Homogeneous  light  is  light  of  only  one 

color.     An  almost  colorless  flame  may  be  pro-        FIG.  225. 
duced  by  burning  pure  alcohol,  or  by  burning 
gas  in  a  Bunsen's  burner.     If  a  platinum  wire  be  dipped 
in  any  salt  of  sodium,  as  common  salt,  and  held  in  a  color- 
less flame,   it  vaporizes  and  yields   a  homogeneous  yellow 
light.     Every  flame  may  be  considered  as  the  combustion 
of  a  body  in  the  state  of  vapor.     Several  other  substances 
yield  characteristic  colored  flames  ;  thus,  strontium  gives  a 
red  color;  potassium,  purple;  copper,  green,  but  the  light 
is  never  perfectly  homogeneous. 

499.  Spectrum   analysis.     The  spectra  formed  by  artifi- 
cial lights  are  usually  wanting  in  several  colors,  but  yield 
the  remainder  with   the  same   refrangibility  as  the   corre- 
sponding colors  in  the  solar  spectrum.     Their  relative  inten- 
sities will  vary  with  the  predominant  colors  of  the  flame. 

N.  p.  is. 


274 


NATURAL   PHILOSOPHY. 


The  spectroscope,  Fig.  226,  is  an  instrument  used  for  analyz- 
ing flames.  The  light  is  admitted  from  the  Bun  sen's 
burner,  E,  through  a  narrow  slit  into  one  end  of  the  tube, 
A,  where  it  is  condensed  by  lenses,  and  thrown  on  the 
prism,  P.  The  refracted  rays  are  thrown  on  the  object 


glass  of  the  telescope,  B,  and  pass  through  it  to  the  eye. 
The  tube,  C,  contains,  at  the  end  nearest  the  prism,  a  lens, 
and  at  the  other  a  scale  divided  into  equal  parts.  When  a 
bright  light  is  placed  in  front  of  the  tube,  C,  it  casts  a 
bright  image  of  the  scale  on  the  prism,  which  is  reflected 
into  the  telescope,  B,  so  that  the  observer  can  n -ad  off  on 
the  scale  the  exact  position  of  the  rays  he  is  observing. 

It'  platinum  wires  an-  dipped  in  solutions  of  the  metals  to  be  ex- 
amined, and  placed  in  tlie  flame  of  the  Bun-en's  burner,  K,  their 
spectra  may  lie  ..(.served  lhn.ii-h  the  t.-lr-n.pc.  !',.  In  this  way  it  M 
found  that  sodium  u'ives  a  bright,  double,  yellow  line,  identical  in 
refraii'/il.ility  with  the  dark  line,  D,  in  the  solar  spectrum.  Potas- 


SPECTRUM  ANALYSIS.  275 

shim  gives  a  red  ray,  in  the  position  of  the  line,  A,  and  a  violet  ray, 
between  G  and  H.  Any  substance  which  can  be  volatilized  will 
furnish  a  spectrum  of  a  few  bright  lines,  which  always  have  the 
same  relative  position.  This  is  also  true  of  incandescent  gases;  hy- 
drogen gives  three  bright  lines,  which  are  identical  in  position  with 
C,  F,  and  G.  These  lines  remain  the  same  throughout  a  great  range 
of  temperature,  and  it  is  highly  probable  that  they  are  not  the  same 
for  any  two  substances.  If  several  substances  are  mixed,  each  will  give 
its  own  system  of  lines,  as  if  it  were  burned  separately.  No  chem- 
ical reaction  is  equal  to  this  as  a  mode  of  detecting  the  presence  of 
many  substances.  It  is,  in  fact,  difficult  to  obtain  a  flame  which  does 
not  show  the  presence  of  sodium,  as  ynnnhrffUTF  °f  a  grain  will  give 
the  characteristic  yellow  line  of  sodium.  Since  the  year  1860,  five 
new  metals  have  been  discovered  by  means  of  the  spectroscope. 
Two  of  these,  coesium  and  rubidium,  are  widely  distributed,  being 
found  in  many  mineral  waters,  and  even  in  tobacco. 

500.  Under  extreme  temperatures  new  lines  are  added 
to  many  spectra;   and,   under  pressure,  hydrogen  may  be 
made  to  yield  a  continuous  spectrum ;  that  is,  one  in  which 
no  dark  lines  are  found. 

Any  incandescent  solid  will  emit,  at  977°  F.,  only  red  rays,  but  as 
the  heat  increases  the  orange  is  added,  and  then  the  other  colors  in 
succession,  until  at  2130°  F.  the  spectrum  becomes  continuous,  con- 
taining all  the  colors,  and,  by  consequence,  the  solid  appears  white 
hot  to  the  naked  eye.  The  lime  light  produced  by  the  oxy-hydrogen 
blow-pipe  affords  a  convenient  method  of  obtaining  a  continuous 
spectrum.  The  electric  spark  ordinarily  gives  a  discontinuous  spec- 
trum, due  both  to  the  metallic  connectors  and  to  the  atmosphere ;  but 
if  the  spark  be  very  intense  the  spectrum  becomes  continuous. 

501.  Absorption   bands.     If  light  which  would  give  a 
continuous  spectrum  is  passed  through  certain  almost  trans- 
parent and  colorless  solutions,   and   then   examined,   dark 
lines  are  found,  which  are  due  to  absorption. 

Thus,  solutions  of  didymium  give  two  dark  lines,  one  in  the  yel- 
low and  the  other  in  the  green.  The  blood  also  produces  two  dark 
lines.  This  effect  is  produced,  not  only  by  light  transmitted  through 
a  dilute  solution,  but  also  when  a  spectrum  is  thrown  on  a  screen 
painted  with  blood. 

The  gases  also  produce  absorption  bands.     Nitrous  acid,  and  the 


276  NATURAL   PHILOSOPHY. 

vapors  of  iodine  and  bromine,  produce  remarkable  series  of  black 
bands.  Even  the  atmosphere  exerts  an  absorptive  power,  which  is 
especially  energetic  when  the  sun  is  near  the  horizon.  Some  of  the 
Fraunhofer's  lines  are  undoubtedly  due  to  the  air,  but  the  larger 
portion  must  have  another  cause. 

502.  If  the  sodium  spectrum  is  formed  in  the  ordinary 
way,  and  the  lime  light  is  transmitted  through  the  sodium 
flames,  a  dark  line  is  seen  in  place  of  the  yellow  sodium 
line,  and  the  spectrum  is  said  to  be  reversed. 

So,  also,  if  two  sodium  flames  are  placed  before  the  spectroscope, 
so  that  one  must  traverse  the  other,  no  spectrum  is  produced.  In 
other  words,  sodium  absorbs  the  same  rays  that  it  emits.  This  is 
found  to  be  the  case  with  so  many  bodies  that  it  may  be  stated  : 

1.  That  every  substance,  when  rendered  luminous,  gives  out  rays  of  a 
definite  degree  of  refrangibility. 

2.  The  same  substance  has  the  power  of  absorbing  rays  of  this  identical 
refrangibility. 

503.  Explanation  of  Fraunhofer's  Lines.    Kirchhoff  sup- 
poses (1.)  that  the  nucleus  of  the  sun  emits  a  continuous 
spectrum,  containing  rays  of  all  degrees  of  refrangibility ; 
(2.)    that   the   luminous   atmosphere   of   the   sun    contains 
vapors  of  various  metals,  each  of  which  would  give  its  own 
system  of  bright  lines ;   (3.)  that  when  the  intense  light  of 
the  nucleus  is  transmitted  through  this  incandescent  atmos- 
phere, the  bright  lines  which  would  have  been  produced  by 
the  atmosphere  are  reversed;    (4.)    that  Fraunhofer's  lines 
are  these  reversed  lines. 

Now,  since  very  many  of  Fraunhofer's  lines  coincide  with  the 
bright  lines  of  metals,  it  is  fair  to  suppose  that  those  metals  exist 
in  the  solar  atmosphere.  Iron  gives  four  hundred  bright  line-  which 
coincide  with  1-Yaunhofer's  lines.  Eighteen  dillercnt  metals  give 
similar  coincidences.  Hence,  we  are  led  to  suppose  that  the  sun  con- 
tains iron,  nickel,  calcium,  magnesium,  chromium,  copper,  sodium, 
aluminum,  hydrogen,  and  a  lew  other  elements.  But  no  evidence 
ha-  been  L'iven  of  the  presence  of  mercury,  silver,  lithium,  gold,  and 
many  others. 

Tin-  -trllar  -p.-ctra  al-o  .-how  .-imilar  coincidences  ;  thu-.  Sinus  and 
Aldebaran  are  thought  to  contain  sodium,  magnoium,  and  hydrogen. 


PROPERTIES   OF   THE  SPECTRUM.  277 

The  comets  and  nebulae  give  spectra  with  bright  lines,  which  seein  to 
show  that  these  bodies  are  incandescent  gases. 

504.  The  properties  of  the  spectrum  are  three;  (1.)  Lu- 
minous; (2.)  Heating;  (3.)  Chemical;  but  all  the  rays  do 
not  possess  them  in  equal  intensity.  The  ordinates  of  the 
curves  in  Fig.  222  show  the  relative  intensity  of  each  prop- 
erty in  a  spectrum  produced  by  a  prism  of  flint  glass. 

1.  The  luminous  intensity  is  greatest  in  the  yellow  and 
least  in  the  violet. 

2.  A  thermometer  placed  in  different  parts  of  the  spec- 
trum will   indicate   an   increase   of   temperature   from   the 
violet  to  the  red. 

The  point  of  maximum  thermal  intensity  varies  with  the  material 
of  the  prism.  By  using  a  prism  of  rock  salt,  which  absorbs  but  little 
heat,  the  point  of  greatest  heating  power  is  found  to  be  beyond  the 
red  rays.  This  fact  shows  that  the  spectrum  contains  dark  rays  of 
heat,  invisible  to  the  eye,  which  are  refracted  less  than  the  red  rays. 

3.  Light  acts  as  a  chemical  agent,  because  it  is  essential 
to   the  healthy  growth  of  plants  and  to  various  chemical 
changes.     Thus  hydrogen  and  chlorine  combine  slowly  in 
diffused  light,  but  with  explosive  violence  in  direct  sun  light. 
The  relative  chemical  effect  of  the  different  rays  may  be  de- 
termined  by  placing   a   film   of  chloride  of  silver  in  the 
spectrum. 

To  accomplish  this,  dip  a  slip  of  paper  in  weak  brine 
made  from  common  salt;  then  dry  the  paper,  and  wash 
one  side  of  it  with  a  solution  of  nitrate  of  silver,  and  dry 
the  paper  again.  A  film  of  chloride  of  silver  will  thus 
be  formed  on  the  paper,  which  will  remain  white  if  the 
operation  be  performed  in  a  darkened  room.  On  exposing 
this  paper  to  the  solar  spectrum,  the  chloride  of  silver  will 
blacken,  but  with  unequal  energy  in  the  different  rays.  A 
quartz  prism  is  best  adapted  for  these  experiments,  because 
L'luss  prisms  absorb  a  large  portion  of  the  chemical  rays. 

The  chemical  effect  is  scarcely  perceptible  in  the  red  and  yellow 
rays;  it  is  decidedly  present  in  the  blue,  and  attains  its  maximum 


278  NATURAL  PHILOSOPHY. 

intensity  in  the  violet.  The  action  extends  even  beyond  the  violet, 
which  shows  that  the  spectrum  contains  rays  more  refrangible  than 
the  violet,  but  not  of  sufficient  intensity  to  be  visible. 

If  these  invisible  ultra-violet  rays  be  concentrated  by  a  quartz  lens, 
they  form  a  faint  beam  of  lavender  colored  light.  These  rays  also 
become  visible  when  they  fall  on  paper  moistened  with  a  solution  of 
quinine,  or  on  glass  colored  with  uranium.  This  property  is  called 
fluorescence,  and  is  due  to  the  power  which  these  substances  have  of 
changing  the  refrangibility  of  the  rays. 

505.  Interference  and  combination,     If  the  wave  theory 
is  correct,  the   luminous  vibrations   must  produce   all  the 
phenomena  of  combination  and  interference,  (377). 

These  phenomena  may  be  shown  in  various  ways.  One  of  the 
simplest  is  that  afforded  by  the  reflection  of  waves  from  both  surfaces 

of  very  thin  plates.  If  a  convex 
lens,  A  B,  Fig.  227,  with  a  long  ra- 
,B  dius  of  curvature,  be  firmly  pressed  on 
a  plane  glass,  D  E,  a  thin  film  of  air 
will  be  inclosed  between  the  two 
glasses,  whose  exact  thickness  at  any 
point  can  easily  be  estimated.  If  a 

beam  of  homogeneous  light  be  allowed  to  fall  perpendicularly  on  the 
upper  surface,  a  portion  will  be  reflected  from  the  convex  surface, 
A  C,  and  another  portion  from  the  plane  surface,  D  E. 

These  two  systems  of  waves  will  intersect  in  crests  and  hollows,  ac- 
cording as  their  paths  differ  by  a  whole  number  of  undulations,  or  by 
an  odd  number  of  semi-undulations.  At  a  certain  distance  from  C,  as 
at  F,  the  two  waves  will  meet  in  opposite  phases  and  destroy  each 
other,  and  the  ring  at  F  will  appear  black.  At  a  greater  distance,  as 
at  G,  the  waves  will  meet  in  the  same  phase  and  increase  the  ampli- 
tude of  vibrations,  and  produce  a  bright  ring  the 
same  color  as  the  light.  Other  points  will  be  found 
beyond  G,  in  which  the  waves  will  meet  in  opposite 
or  similar  phases,  and,  consequently,  a  series  of  black 
and  colored  rings  will  be  formed  about  the  center, 
C.  If  the  yellow  sodium  flame  is  employed,  \ve 
shall  have  alternately  black  and  yellow  rings;  if 
red  light  l>e  employed,  a  similar  system  of  red  and  black  rings  is 
produced,  and  so  on  for  other  colors. 

506.  If  solar  light  be  employed,  each  rin^  contains  all 


INTERFERENCE. 


279 


the  colors  of  the  spectrum  in  order,  from  violet  on  the  inner 
edge  to  red  on  the  outer,  because  the  different  colors  have 
different  refrangibilities,  and  the  rings  are  not  exactly  super- 
imposed. The  smallest  rings  are  the  most  brilliant,  because 
the  vibrations  coincide  the  most  frequently. 

These  rings  are  known  as  Newton's  rings,  and  by  finding  the  thick- 
ness of  the  layer  of  air  between  the  glasses,  the  following  table  has 
been  constructed : 


Colors. 

Lengths  of  waves 
in  parts 
of  an  inch. 

Number  of  waves 
in  an  inch. 

Number  of  waves  in  a 
second. 

Extreme  red  

.0000266 

37640 

442000000000000 

Red 

0000956 

39180 

458000000000000 

Orange  

.0000240 

41610 

489000000000000 

Yellow    .  .    . 

0000227 

44000 

517000000000000 

0000211 

47460 

558000000000000 

Blue  ... 

0000196 

51110 

599000000000000 

Indigo 

0000185 

54070 

634000000000000 

Violet  

0000174 

57490 

675000000000000 

Extreme  violet 

0000167 

59750 

702000000000000 

507.  Similar  phenomena  of  interference  may  be  observed 
in  other  very  thin  plates,  as  in  mica,  soap  bubbles,  or  in  the 
film  of  oil  on  water,  or  alcohol  on  glass.     Striated  surfaces, 
formed  by  very  fine  parallel  grooves,  reflect  bright  colors 
for  the  same  reason.     This  is  the  cause  of  the  iridescence 
of  mother  of  pearl,  of  labradorite,  and  of  the  changeable 
hues  in  the  plumage  of  birds  and  the  scales  of  insects. 

508.  Diffraction.     When  a  pencil  of  light  encounters  an 
obstacle,  the  rays  diverge  from  the  edge  of  the  obstacle  as 
if  from  a  new  point.      The  light  then  enters  the  shadow  of 
the  obstacle,  and  is  said  to  be  diffracted.     If  a  thin  body,  as 
a  hair,  is  placed  in  a  small  opening,  the  diffracted  rays  cross 
each  other  and  produce  fringes  of  colored  light,  which  are 
due   to   interference.     Light   is  always   diffracted   when   it 
passes  the  edge   of  an   object,   but  it   is   rarely  observed, 
because   the   fringes   are   illuminated  by   light  from   other 
sources,  and  quenched. 


280  NATURAL   PHILOSOPHY. 

509.  The  color  of  light  is  determined  by  the  frequency 
of  its  vibrations,  and  its  brightness  by  the  amplitude  of  its 
vibrations. 

The  heating,  luminous,  and  chemical  rays  of  the  spectrum 
are  the  same  in  kind,  and  differ  from  each  other  only  as  red 
differs  from  violet ;  that  is,  in  degree  of  refrangibility  and 
rapidity  of  vibration.  The  retina  of  the  human  eye  is  so 
constructed  that  only  rays  of  medium  refrangibility  and 
rapidity  excite  the  fibers  of  the  optic  nerve  to  vibration. 
The  appreciation  of  color  varies  greatly  with  different  indi- 
viduals, but  the  reason  of  this  is  not  yet  understood. 

From  observations  made  in  animals,  it  would  seem  that 
certain  fibers  of  the  optic  nerve  are  sensitive  to  one  color, 
and  others  to  another.  The  eye  which  is  defective  in  these 
fibers  is  color  blind,  or  unable  to  distinguish  colors  appro- 
priate to  the  lacking  nerve  fibers.  Dalton  could  not  distin- 
guish blue  from  crimson  ;  others  confound  different  colors, 
and  some  can  not  distinguish  colors  at  all,  and  yet  in  every 
other  respect  their  sight  is  perfect. 

510.  The  natural  color  of  a  body  is  due  to  the  power  it 
has   of  extinguishing   certain   vibrations  and    reflecting  or 
transmitting  others.     A  white  screen   placed    in   the  solar 
spectrum  appears  of  all  the  colors.     A  red  screen  appears 
brighter  red   in  the  red  rays  of  the  spectrum,  and  almost 
black  in  the  blue.     A  red  object  can  reflect  only  red  rays, 
and  absorbs  the  rest.     Hence,  the  color  of  an  opaque  body 
is  due  to  the  light  which  it  reflects.     A  body  that  reflects 
all  the  rays  of  the  solar  spectrum  is  white;   a  body  that 
reflects  no  light,  or  but  very  little,  is  black.     Most  natural 
colors  of  bodies,  when  examined  by  the  prism,  are  found  to 
be  compound. 

If  all  the  solar  \\y\\\  is  transmitted  by  a  transparent  body  it  appears 
colorless.  If  it  absorbs  some  of  the  rays,  the  emergent  liirht  will 
be  of  the  color  produced  by  tin-  transmitted  vibrations.  Thus,  red 
<fl;ts-  transmits  a  nearly  li<tmn^cnr.iu>  red.  An  ammoniaral  solution 
Of  OZide  Of  OOpper  iran-mit-  a  v.-ry  pure  blue.  Some  bodies  reflect 


THE  RAINBOW.  281 

one  color  and  transmit  another;  thus,  gold  appears  yellow  by  reflected 
light  and  green  by  transmitted  light. 

511.  The  rainbow  is  due  to  the  combined  effect  of  re- 
flection, refraction,  dispersion,  and  interference  of  the  solar 
rays  in  passing  through  drops  of  rain.     For  its  formation, 
it  is  necessary  (1.)  that  the  sun  shall  shine  during  a  shower, 
(2.)  that  the  observer  shall  stand  with  his  back  to  the  sun, 
between  the  drops  of  rain  and  the  sun.     When  two  bows 
are  visible,  the  inner  and  brighter  is  called  the  primary  bow, 
the  outer,  the  secondaiy  bow.     Each  bow  contains   all  the 
prismatic  colors,  so  arranged  that  in  the  primary  bow  the 
red  band   is   on  the  outside,  and  in  the  secondary  bow  on 
the  inside.     The  common  center  of  both  arches  is  always 
in  the  prolongation  of  a  line  drawn  from  the  sun  through 
the  eye  of  the  observer.     Fig.  230. 

512.  The  formation  of  the  primary  bow  may  be  ex- 
plained by  tracing  the  course  of  the  sun's  rays  through  a 
drop  of  rain. 

Suppose  the  paraUel  rays  of  the  sun,  S  S'  S"  S'",  to  fall 


FIG.  229. 


on  the  rain  drop.  The  ray,  SI,  which  falls  perpendicu- 
larly on  the  drop  will  suffer  no  refraction,  but  will  be  par- 
tially reflected  back,  as  it  enters  and  leaves  the  drop,  in 


282 


NATURAL   PHILOSOPHY. 


the  line,  S  I.  Any  ray  of  little  obliquity  to  the  surface 
of  the  drop,  as  ST,  will  be  refracted  to  if,  where  it 
will  be  reflected  to  R',  and  then  again  refracted  in  the 
direction  R'  E',  making  a  small  angle  with  the  incident 
ray,  ST.  The  angle  of  deviation  between  the  incident 
and  emerging  rays  will  increase  until  we  reach  a  ray,  S"  I", 
about  59°  from  the  axis,  for  which  the  deviation,  S"  V  E", 
is  the  greatest  possible. 

Beyond  this  limit  the  deviation  of  the  emergent  rays 
will  again  diminish,  until  we  reach  the  ray,  S'"  I'",  which 
is  tangent  to  the  top.  Hence,  of  the  incident  rays  near  the 
limit  of  59°,  those  above  V  will  emerge  very  nearly  parallel 
to  those  below.  The  rays  of  the  sun  are  thus  dispersed  by 
each  refraction  as  by  a  nearly  spherical  prism,  but  will  be 
more  intense  in  the  direction  of  the  parallel  rays,  R"  E",  so 
that  these  only  will  bring  to  the  eye  the  impression  of  color. 
Owing  to  the  difference  in  the  refraction  of  the  different 
rays,  the  line  of  greatest  intensity  is  not  the  same  for  the  differ- 
ent colors.  For  the  red  ray,  the  angle,  S"  VE",  between  the 

incident  and  emergent 
pencils  is  about  42°;  for 
the  violet,  about  40°, 
and  for  the  other  colors 
between  these  limits. 

If,  nowT,  the  line, 
s  o  c,  Fig.  229,  be  con- 
ceived to  pass  from  the 
sun  through  the  eye  of 
the  observer,  the  angles 
S"  V  o  and  V  o  C,  are 
equal,  because  the  solar 
rays  arc  parallel. 
Hence,  if  the  eye  bo 

Flo  taken     as    the    center, 

the  red  rays  will  all  be 

seen  in  a  circle  of  42°  null  us  :   the  violet  rays  in  a  circle  of 
40°    radius,    and    the    other   colors  between    these.     As  the 


THE  SECONDARY  BOW.  283 

emergent  rays  are  nearly,  but  not  exactly  parallel,  they 
will  be  in  a  condition  to  combine  and  interfere,  and  will,  of 
course,  give  rise  to  colored  bands  separated  by  dark  spaces. 
The  colors  are  much  brighter  by  reason  of  combination, 
and  purer  by  reason  of  interference,  because  a  dark  band 
separates  each  color  from  the  other.  The  second  band  of 
each  color  is  sometimes  bright  enough  to  be  visible,  and 
then  forms  a  spurious  bow  below  the  primary. 

513.  The  secondary  bow  is  due  to   two  reflections  and 
two  refractions.     In  order  that  the  rays  may  descend  to  the 
observer,  the  incident  rays 
must  enter  below  the  axis 
of  the   drop,    as   in  Fig. 
231.     Only  the  rays  which 
enter  at  a  distance  of  about 
71°   below   the   axis,   will 
emerge  sufficiently  parallel  ^ 

to  give  a  bright  color  at  a 

great  distance.  The  red  band  has  a  radius  of  about  51°, 
and  the  violet  about  54°.  As  some  light  is  lost  at  each 
reflection,  the  secondary  bow7  is  fainter  than  the  primary. 

The  extent  of  the  bow  depends  on  the  position  of  the  sun.  When 
the  sun  is  in  the  horizon,  the  arches  are  semicircles;  as  it  rises 
they  diminish,  the  primary  bow  ceasing  when  its  altitude  is  about 
42°,  and  the  secondary  when  about  54°.  If  the  sun  is  at  or  a  little 
below  the  horizon,  and  the  observer  is  sufficiently  elevated,  a  com- 
plete circle  may  be  rendered  visible.  Such  circular  rainbows  are 
often  observed  near  waterfalls  and  fountains. 

Faint  lunar  rainbows  are  sometimes  seen.  The  halos  seen  about  the 
sun  and  moon  are  supposed  to  be  due  to  light  refracted  by  minute 
crystals  of  ice  suspended  in  the  air. 

514.  Recapitulation. 

When  solar  light  is  examined  by  a  prism,  it  is  found  to  consist  of 
seven  primary  colors,  which  are  interrupted  by  dark  lines. 

Other  luminous  bodies  yield  spectra  which  resemble  the  solar  spec- 
trum in  many  particulars. 


NATURAL    PHILOSOPHY. 

All  spectra   have  luminous,  thermal,  and  chemical  properties,  but 
not  in  equal  intensity. 

The  spectrum  analysis  depends  on  the  fact  that  every  luminous 
body  emits  rays  of  definite  refrangibility. 

The  dark  lines  are  explained  by  the  fact  that  every  luminous  body- 
is  capable  of  absorbing  the  rays  which  it  emits. 

Luminous  vibrations  may  be  made  to  combine  and  interfere  by  re- 
flection, refraction,  and  diffraction. 

Colors  are  dependent  on  the  frequency  of  the  luminous  vibrations. 
VISION    AND    OPTICAL    INSTRUMENTS. 

515.  Camera  obscura.  One  form  of  this  instrument  has 
already  been  described  in  section  444.  The  photographer's 
camera,  Fig.  232,  is  constructed  on  the  same  principle. 
The  box,  C,  is  the  dark  chamber.  The  screen,  E,  is  of 
ground  glass,  inserted  in  the  movable  frame,  B.  An  achro- 

D 


FlG.  232. 


matic  convex  lens  is  placed  in  the  tube,  A,  in  order  to 
render  the  image  clear  and  well  defined.  The  focus  may 
!><•  adjusted  t<>  ol.jeets  at  different  distances  l>v  moving  th',- 
screen,  or  the  lens  backward  or  forward.  The  image  will 
be  real,  and  smaller  than  the  object,  because  the  object  is 
placed  more  than  twice  the  focal  distance  in  front  of  the 
lens. 


THE  HUMAN  EYE.  285 

516.  The  draughtsman's  camera  is  used  for  sketching 
natural  scenery.  The  student  can  readily  make  an  instru- 
ment of  this  kind  by  inserting  a  convex  spectacle  glass 
in  an  orifice  at  the  top  of  a  box,  about  two  feet  high,  and 
placing  a  plane  mirror  at  an  angle  of  45°,  so  as  to  reflect 
the  light  from  external  objects  downward  through  the 
lens.  The  image  can  be  received  on  a  paper  at  or  near 
the  bottom  of  the  box.  A  shawl  must  be  throwrn  over  the 
open  side  of  the  box,  in  order  to  shut  out  the  extraneous 
light. 


517.  The  human  eye  is  very  nearly  spherical,  and  is 
about  an  inch  in  diameter.  It  consists  essentially  of  (1.) 
three  enveloping  coats,  and  (2.)  three  refracting  bodies. 
Fig.  233  presents  these  parts  in  horizontal  section. 

(1.)  The  outer  coat,  or  white  of  the  eye,  is  a  tough  and 
opaque  membrane  called  the  sclerotic.  In  the  front  part  of 
this,  the  transparent  cornea,  a,  is  set  in  like  a  watch-glass. 

The  middle  coat,  k,  is  the  choroid,  which  consists  of  a 
membrane,  abundantly  supplied  with  blood-vessels,  and 
covered,  on  its  inner  face,  by  a  dark,  velvety  substance, 
called  the  black  pigment. 

The  inner  coat  is  the  retina,  m,  which  is  mainly  an  ex- 
pansion of  the  optic  nerve,  n,  with  the  addition  of  terminal 


286  NATURAL   PHILOSOPHY. 

nerve  elements  for  the    perception  of  light,  spread  out  in 
very  fine  net-work  on  the  black  pigment. 

Near  the  junction  of  the  cornea  and  sclerotic,  the  choroid 
becomes  thicker,  and  terminates  in  the  ciliary  processes.  To 
the  outer  portion  of  these  is  attached  an  opaque,  contractile 
membrane,  d,  called  the  iris,  because  it  is  the  colored  por- 
tion of  the  eye.  The  iris  is  pierced  by  an  aperture,  called 
the  pupil,  through  which  the  luminous  rays  pass  to  the 
bottom  of  the  eye. 

(2.)  Behind  the  iris,  and  supported  by  a  suspensory  liga- 
ment, attached  to  the  ciliary  muscle  which  proceeds  from 
the  ciliary  processes,  is  the  crystalline  lens,  f.  This  is  a 
double  convex  lens,  having  its  anterior  face  of  less  con- 
vexity than  the  posterior. 

The  portion  of  the  eye,  e,  between  the  cornea  and  the 
crystalline,  is  filled  with  a  thin  liquid,  called  the  aqueous 
humor. 

Behind  the  crystalline  is  the  chamber,  h,  which  is  filled 
with  a  jelly-like  liquid,  called  the  vitreous  humor.  The 
humors  and  the  crystalline  are  each  surrounded  by  a  deli- 
cate membrane,  or  capsule. 

518.  If  a  luminous  point  be  placed  before  the  eye,  the 
central  rays  pass  through  the  cornea,  and  enter  the  aqueous 
humor.  Of  these  rays,  the  more  divergent  are  intercepted 
by  the  iris,  and  only  those  which  are  nearly  parallel  are 
admitted  through  the  pupil  to  the  interior  of  the  eye. 
These  are  transmitted  through  the  crystalline  and  the  vit- 
reous humor,  and  finally  fall  upon  the  retina. 

The  effect  of  these  refracting  bodies  will  be  the  same  as 
that  of  a  converging  system  of  lenses,  and  they  will,  there- 
fore, tend  to  form,  at  or  very  m-ar  the  retina,  an  iinauc  of  tin- 
luminous  point.  The  same  being  true  of  all  diverging  pencils 
proceed  in. i:  from  an  object,  then-  will  be  Conned  on  the  retina 
an  image  of  the  object,  which  will  be  inverted,  becaii-e  the 
a.\c.-  of  the  pencil.-  cross  each  other  before  reaching  the  ret- 


VISION.  287 

ina.  The  mechanical  action  of  the  eye  is  very  similar  to 
that  of  the  photographer's  camera. 

519.  The  sensation   of   sight   is   due   to   the  impression 
made  by  the  image  on  the  terminal  percipient  nerve  ele- 
ments of  the  retina,  and  thence  conveyed  by  the  optic  nerve 
fibers  to  the  brain.     These  nerve  elements  are  contained  in 
u   layer   next   the   black  pigment,    and   consist  of  a  great 
number  of  very  minute  bodies,  arranged  side  by  side,  and 
resembling  rods  and  cones,  standing  perpendicularly  to  the 
surface  of  the  retina.     It  is  supposed  that  the  waves  of  light 
falling  upon  this  layer  of  rods  and  cones  produce  vibrations, 
which  are  conducted  by  the  nerve  fibers  in  such  a  way  to 
the  brain  that  it  is  excited  and  acknowledges  the  reception 
of  the  luminous  image  on  the  retina. 

520.  The  impression  made  on  the  retina  is  not  instan- 
taneous, and  when  once  made  continues,  on  the  average,  for 
nearly  one-third   of  a  second   after  the  exciting  cause  has 
ceased   to   act.     If,  therefore,   an   ignited   coal   be  whirled 
about  rapidly,  luminous  rings  are  produced. 

Many  optical  toys  owe  their 
effect  to  the  duration  of  the 
impression  on  the  retina.  The 
Thaumatrope,  or  "twirl  me 
round,"  Fig.  234,  consists  of  a 
card  which  is  made  to  revolve 
by  means  of  strings  attached  to  FIG. 

its  siiit'-.     A    horse    may  be  so 

painted  on  one  side  and  a  rider  on  the  other,  that  a  rapid  revolution  of 
the  card  will  cause  the  rider  to  appear  seated  on  the  horse.  The  same 
principle  is  applied  in  the  familiar  Zoetrope,  by  which  an  object  painted 
in  different  positions  appears  to  perform  the  motions  of  real  life. 

521.  The  accommodation  of  the  eye  to  different  distances 
is  effected  by  the  action  of  the  ciliary  muscle  upon  the  crys- 
talline lens.    When  the  eye  is  turned  toward  a  distant  object, 
the  muscle  relaxes  and  the  lens  is  flattened;  but,  for  near 
objects,   the  muscle   contracts  and  the  lens  becomes  more 


288  NATURAL   PHILOSOPHY. 

convex.  In  this  way,  the  conjugate  focus  of  the  object  is 
made  always  to  fall  upon  the  retina.  The  power  of  accom- 
modation is  very  great,  and  is  exerted  unconsciously  with 
marvelous  rapidity.  Nevertheless,  there  is  for  all  eyes  a 
certain  distance  at  which  the  parts  of  an  object,  as,  for 
instance,  the  letters  on  this  page,  are  seen  with  most  dis- 
tinctness. This  distance,  which  varies  for  ordinary  eyes 
from  five  to  ten  inches,  is  called  the  distance  of  distinct 
vition. 

522.  The  limits   of  distinct   vision.     In  order  that  an 
object  may  appear  distinct,  the  rays  proceeding  from  it  must 
enter  the  eye  nearly  parallel.     If  rays  diverge  from  a  point 
more  than  eighteen  inches  from  the  eye,  those  that  enter 
the  eye  will  be  sensibly  parallel.     The  nearer  the  object  is 
to  the  eye,  the  more  perfect  will  be  the  image,  provided 
always  that  the  rays  are  brought  to  a  focus  on  the  retina. 
If  a  printed  page  be  brought  too  close  to  the  eye,  the  letters 
appear   more  or  less  blurred,  because  the  rays  are  too  di- 
vergent to  focus  on  the  retina.     For  normal  eyes,  the  far- 
thest point  of  distinct  vision  is  infinitely  distant,  the  nearest 
point  about  three  and  one-half  inches.     Far-sighted  eyes  are 
those  whose   nearest   point  of  distinct  vision   exceeds   ten 
inches,  and  near-sighted  eyes  are  those  whose  farthest  point 
of  distinct  vision  is  at  a  finite  distance,  varying  from  three 
inches  to  twenty  feet. 

523.  The  normal  eye  is  very  nearly  round,  and  the  prin- 


Fio.  235. 


cipal    focus  of   parallel    r:iy>    falls    <>n    tho    retina,    as   at   E, 
Fig.  235.      From  this  figure  there  are  two  principal  devia- 


DEFECTS   OF   THE  EYE.  289 

tions,  producing  what  are  known  as  Myopic  and  Hyperme- 
ti-njilc  vision.  The  myopic  eye  is  an  oblate  spheroid,  in 
which  the  retina,  M,  lies  beyond  the  focus  of  parallel  rays. 
For  this  cause,  only  divergent  rays  are  brought  to  focus  on 
the  retina,  and  thus  near-sightedness  results.  Such  eyes  will 
obtain  relief  by  the  use  of  concave  glasses. 

The  hyperraetropic  eye  is  a  prolate  spheroid,  in  which  the 
retina,  H,  lies  in  front  of  the  focus  of  parallel  rays.  Hence, 
only  the  convergent  rays  come  to  a  focus  on  the  retina,  and 
far-sightedness  results.  When  such  eyes  deviate  but  little 
from  the  normal,  the  power  of  accommodation  may  be  suffi- 
ciently active  to  produce  perfect  vision,  but  in  other  cases 
they  will  require  the  use  of  convex  glasses. 

There  are  other  anomalies  of  refraction  in  the  eye,  among 
which  astigmatism  is  the  most  common.  Persons  so  affected 
find  it  difficult  to  see  horizontal  and  vertical  lines  distinctly 
at  the  same  moment.  The  glasses  used  to  correct  astigma- 
tism are  cut  from  cylindrical  surfaces  instead  of  spherical. 

Another  defect  of  the  eye  is  called  presbyopia,  because  it 
is  generally  found  only  in  old  persons.  This  results  from  a 
gradual  diminution  of  the  elasticity  of  the  crystalline  lens, 
by  reason  of  which  the  power  of  accommodation  is  weak- 
ened, and  only  distant  objects  are  seen  distinctly.  This  kind 
of  far-sightedness  may  also  be  remedied  by  the  use  of  convex 
glasses.  * 

524.  Magnifying  glasses.  If  an  object  be  very  minute, 
the  image  formed  on  the  retina  will  be  too  small  to  affect 
the  optic  nerve.  If  the  object  be  too  near,  the  rays  will  not 
focus  on  the  retina,  because  they  are  too  divergent.  Suppose 
a  pin  hole  to  be  pricked  in  a  thin  card  and  placed  between 
the  eye  and  a  printed  page.  Now,  if  the  page  be  brought 


*  It  will  at  once  be  seen  that  it  is  an  error  to  suppose  that  presbyopia  is 
due  to  the  flattening  of  the  cornea,  and  that  all  treatment  based  on  this 
theory  is  absurd.  Either  of  the  defects  mentioned  may  be  relieved  by  the 
use  of  spectacles ;  but  as  there  is  great  danger  of  injuring  the  eye  by  the 
abuse  of  spectacles,  the  glasses  suitable  for  each  case  should  be  selected 
only  by  competent  oculists. 
N.  P.  19. 


290  NATURAL  PHILOSOPHY. 

very  close  to  the  eye,  the  outer  divergent  rays  will  be  ex- 
cluded, and  the  eye  will  be  able  to  converge  the  few  nearly 
parallel  rays  to  a  focus,  and  thereby  form  a  faint  but  distinct 
image.  At  the  same  time,  the  letters  will  appear  magnified, 
because  the  visual  angle  is  increased. 

A  convex  lens  placed  a  little  nearer  the  object  than  its 
focal  distance  will  converge  all  the  rays  on  the  retina,  thus 
preserving  all  the  light  while  it  magnifies  the  object  by  in- 
creasing the  visual  angle.  Since  the  lens  may  be  held  close 
to  the  eye,  the  magnifying  power  may  be  found  by  dividing 
the  distance  of  distinct  vision  by  the  focal  distance  of  the 
lens. 

Thus,  if  a  lens  have  a  focal  distance  of  one-half  an  inch,  and  the 
distance  of  distinct  vision  be  assumed  as  ten  inches,  the  lens  will 
magnify  twenty  times  in  diameter  or  four  hundred  times  in  area. 
Lenses  have  been  made  having  a  focal  distance  of  •£-$  of  an  inch,  and 
a  consequent  magnifying  power  of  five  hundred  diameters. 

With  a  powerful  lens,  the  object  must  be  very  near  the 
surface ;  consequently,  only  the  smallest  portion  of  the  object 
will  be  seen ;  hence,  the  field  of  view  diminishes  as  the  mag- 
nifying power  increases.  Moreover,  from  the  great  nearness 
of  the  object,  the  outer  rays  are  so  diverging  as  to  cause 
spherical  aberration ;  for  this  reason,  only  the  central  por- 
tion of  a  lens  can  be  used,  and  this  is  termed  its  aperture. 

The  diamond  has  nearly  twice  the  refracting  power  of  glass,  and 
hence  the  same  magnifying  power  can  be  attained  with  a  lens  of  less 
curvature,  and  is  consequently  less  subject 
to  spherical  aberration  than  those  of  glass. 
comParative  thicknesses  and  curva- 
Flo  ggg  tures  of  three  lenses  having  the  same  mag- 

nifying   power    are    shown    in    Fig.   236. 

The  loss  of  light  by  absorption  is  in  proportion  to  the  thickness  of 
the  lens,  and  also  to  the  size  of  the  aperture.  The  illuminating  power 
of  a  lens  is  the  amount  of  light  it  eollert-  from  tin-  ohjeet  and  trans- 
mits to  the  eye;  hence,  as  hi^h  magnifying  powers  require  small 
apertures,  their  illuminating  powers  arc  feeble  and  require  that  the 
illumination  of  the  object  should  be  intense.  This  is  effected  by  con- 
•  len-iin^  the  solar  li^ht  upon  it  l>y  means  of  a  concave  mirror,  or  by 
a  large  convex  lens. 


THE  STEREOSCOPE. 


291 


From  these  considerations,  it  follows  that  microscopes  of  different 
local  distances  are  required  for  different  purposes.  The  magnifying 
glasses  used  for  viewing  pictures  afford  a  large  field  of  view  and 
magnify  but  little;  the  smaller  glasses  used  by  watchmakers  are 
of  greater  magnifying  power.  Pocket  microscopes  usually  contain 
two  or  three  lenses,  acting  as  a  single  thick  lens.  They  do  not 
usually  magnify  more  than  from  five  to  ten  diameters. 

525.  The  stereoscope.  If  a  solid  object,  as  a  die,  be 
held  a  short  distance  before  the  eyes,  each  eye  will  see  the 
object  from  a  different  point  of  view ;  and,  consequently, 


. 


/ 


FIG.  237. 


the  two  images  formed  on  the  retina  will  not  be  exactly 
alike.  Fig.  237  represents  a  die  as  seen  by  the  left  and 
right  eyes  respectively.  By  the  blending  of  these  two 
images,  the  object  appears  solid.  This  effect  will  be  pro- 
duced in  the  engraving,  if  a  card  be  held  between  the  two 
figures,  and  they  are  steadily  looked  at 
for  a  few  seconds,  one  by  the  right  eye 
and  the  other  by  the  left.  The  stereo- 
scope, Fig.  238,  is  contrived  to  assist 


FIG.  238. 


FIG.  239. 


the  eye  in  blending  two   slightly  different  pictures  of  the 


292 


NATURAL   PHILOSOPHY. 


same  object,  taken  from  points  of  view  related  to  each  other 
in  the  same  manner  as  the  two  eyes  of  the  observer. 
These  pictures  are  placed  in  the  bottom  of  a  box  and 
viewed  through  two  eye  pieces,  which  are  segments  cut 
from  a  double  convex  lens.  A  diaphragm,  D,  Fig.  239, 
prevents  each  eye  from  seeing  more  than  one  picture. 
The  rays  of  light  from  A,  after  emerging  from  the  lens, 
M,  reach  the  eye  as  if  they  came  from  C,  while  rays  from 
B,  after  emerging  from  N,  appear  also  to  come  from  C. 
Thus  the  two  pictures  are  blended  in  one,  and  appear  to 
come  from  a  solid  object  at  C. 

526.  The  magic  lantern  is  an  instrument  by  which  trans- 
lucent objects   are   magnified  and   thrown    upon   a  screen. 


—  FlO.  240. 

A  lamp  is  placed  in  the  common  focus  of  a  reflector,  MN, 
and  of  a  convex  lens,  A,  so  that  a  strong  beam  of  light  is 
thrown  on  the  object  inserted  in  the  slit,  C  D.  The  magni- 
fying lens  forms  an  image  of  the  object  on  the  screen,  E  F, 
placed  at  its  conjugate  focus.  The  objects  are  usually 
painted  on  glass,  but  the  instrument  may  also  be  used  to 
magnify  photographs  on  glass,  or  natural  translucent  ob- 
jects, as  the  wings  of  insects  pasted  on  glass. 

The  image  may  be  made  as  large  as  is  desired,  by  adjust- 
ing the  lens,  B,  but  as  the  brightness  of  the  image  dimin- 
ishes in  proportion  as  the  object  is  enlar<r<'<l,  strong  illu- 
niiiiatinLr  I>"\V<T  must  be  used.  The  electric  and  the  linn: 
liirht  arc  sometimes  used.  The  solar  microscope  is  essentially 
a  magic  lantern,  illuminated  by  the  sun. 


THE   COMPOUND   MICROSCOPE.  293 

The  phantasmagoria  and  dissolving  views  of  the  showmen 
are  obtained  by  combining  the  effects  of  two  lanterns,  whose 
focal  distances  are  readily  adjusted. 

527.  The  compound  microscope  consists  of  an  object 
glass,  or  objective,  M,  of  short  focus,  and  an  eye  glass,  N, 
of  less  magnifying  power.  The  object,  A  B,  is  placed  a 
little  beyond  the  focus  of  the  objective,  and  its  real  image, 
a  b,  inverted  and  magnified,  is  formed  a  little  within  the 
focus  of  the  eye  glass.  By  this  glass  the  real  image  is 


v ,...,, 


viewed  as  by  a  simple  microscope,  and  hence  forms  another 
image,  a'  b',  which  is  still  more  magnified,  and  is  virtual. 
The  magnifying  power  is  equal  to  the  product  of  the  mag- 
nifying powers  of  the  two  glasses ;  if  the  objective  magnifies 
fifty  diameters,  and  the  eye  piece  ten  diameters,  the  total 
magnifying  power  is  five  hundred  diameters.  The  advan- 
tage of  this  form  of  microscope  is,  that  a  comparatively 
large  field  of  view  may  be  attained  with  high  magnifying 
power. 

To  attain  a  larger  field  of  view,  and,  at  the  same  time,  correct  the 
errors  arising  from  spherical  and  chromatic  aberrations,  both  the 
objective  and  the  eye  glass  are  frequently  composed  of  two  or  more 
lenses,  but  each  combination  acts  as  a  single  lens. 

The  difference  between  the  simple  and  compound  microscopes  con- 
sists not  in  the  number  of  glasses  employed,  but  in  this,  that  in  the 
simple  microscope  the  object  is  viewed  directly,  and  in  the  compound 
microscope  a  real  magnified  image  of  the  object  is  viewed  by  a  com- 
mon magnifier. 

528.  The  telescope  is  used  for  viewing  distant  objects. 
A  real  image  of  the  object  is  first  formed  in  the  principal 
focus  of  a  concave  mirror,  or  of  a  convex  lens  ;  and  this 


294  NATURAL    PHILOSOPHY. 

image,  which  is  always  smaller  than  the  object,  is  then 
magnified  by  an  eye  glass,  in  the  same  manner  as  by  a 
simple  microscope.  In  the  refract  in<j  trl<*<-ope  the  image  is 
formed  by  an  object  glass  of  small  convexity ;  in  the  reflect- 
ing telescope,  by  a  concave  mirror. 

529.  The  astronomical  telescope  consists  of  the  object 
glass,  M,  and  the  eye  glass,  N.  The  object  glass  forms  an 
inverted  image,  b  a,  of  the  distant  object,  A  B,  in  its  prin- 
cipal focus,  F ;  this  image  is  then  viewed  by  the  eye  glass, 


FIG.  IML'. 

N,  which  is  so  placed  as  to  receive  the  image  at  a  distance 
a  little  less  than  its  own  focal  length.  If  the  eye  were 
placed  at  the  center  of  the  object  glass,  it  would  see  the 
object  and  the  image  under  the  same  visual  angle,  and  con- 
sequently of  the  same  size ;  but  by  means  of  the  eye  glass, 
the  image  appears  as  much  larger  as  the  focal  length  of  the 
eye  glass  is  less  than  the  focal  length  of  the  object  glass. 
Hence,  the  magnifying  power  of  a  telescope  is  found  by 
dividing  the  focal  distance  of  the  object  glass  by  that  of  the 
eye  glass. 

The  object  glass  should,  therefore,  be  of  small  convexity,  that  its 
focal  distance  may  be  as  great  as  possible,  and  the  eye  glass  should 
be  of  great  convexity,  because  the  magnifying  power  depends  on  it. 
Great  magnifying  power  requires  a  sufficient  illuminating  power  in 
the  object  glass.  For  this  reason  the  object  glass  should  have  as 
LT.-at  area  as  possible,  in  order  to  render  the  real  image  brighter. 
The  telescope  in  the  Chicago  observatory  has  an  object  glass  eighteen 
inches  in  diameter;  it,  therefore,  takes  in  at  least  live  thousand  times 
more  light  than  the  pupil  of  the  naked  eye. 

A  telescope  recently  constructed  in  England  has  an  object  glass 
twenty-five  inches  in  diameter.  It  is  the  largest  refracting  telescope 
in  the  world. 

An  astronomical  telescope  is  called  an  o///./i//»/-/<//  when  it  is  so 
mounted  that  it  IWMfM  ea-t  or  W&t  in  the  heavens  parallel  to  the 


THE   TELESCOPE. 


295 


earth's  equator.  It  is  moved  by  clock  work,  so  that  when  it  is  once 
directed  toward  a  fixed  star  it  compensates  for  the  diurnal  revolution 
of  the  earth,  and  keeps  the  star  constantly  in  the  field  of  view. 

530.  The  terrestrial  telescope.  The  inversion  of  the 
image  in  the  astronomical  telescope  is  of  little  moment  in 
viewing  heavenly  bodies,  but  would  be  a  serious  inconveni- 
ence for  terrestrial  objects.  The  terrestrial  telescope  has, 
therefore,  two  additional  lenses  for  rendering  the  image 
erect.  Two  convex  glasses,  P  and  Q,  are  so  placed  that 
the  lens,  P,  renders  the  rays  diverging  from  the  image,  6  a, 
formed  by  the  object  glass,  M,  parallel  to  each  other.  After 


FIG.  243. 

crossing  at  H,  these  rays  again  converge  in  the  focus  of  the 
eye  glass  and  form  an  image,  a'  &',  inverted  with  respect  to 
the  first  image,  but  erect  with  respect  to  the  object.  This 
second  image  is  then  magnified  in  the  ordinary  manner  by 
the  eye  glass,  R.  The  magnifying  power  is  the  same  as  in 
the  astronomical  telescope,  provided  the  correcting  glasses, 
P  and  Q,  have  equal  focal  length,  but  the  absorption  of 
light  is  much  greater. 

531.  Galileo's  telescope  consists  of  a  convex  object  glass 
and  a  concave  eye  glass.  The  object  glass  tends  to  form  a 
real  but  inverted  image  at  b  a ;  but  the  rays  converging  to 


FIG.  244. 


this  image,  as  Mot,  O  a,  are  intercepted  by  the  eye  glass, 
If,  which  is  placed  at  its  focal  distance  in  front  of  the  image, 
and  after  refraction  appear  to  diverge  from  the  points  a'  and 
b'.  Hence,  the  object  will  appear  erect,  and  as  much  larger 


296  NATURAL   PHILOSOPHY, 

than  the  object  as  the  focal  length,  O  F,  of  the  convex  lens 
exceeds  the  focal  length,  O'  F,  of  the  concave  lens. 

The  length  of  the  astronomical  telescope  equals  the  sum  of  the 
focal  lengths  of  the  two  glasses,  but  that  of  the  Galilean  telescope 
equals  the  difference  of  the  focal  lengths:  hence,  the  Galilean  tele- 
scope may  be  made  short  and  portable.  The  field  of  view  is  much 
limited,  because  only  the  central  portion  of  the  emergent  rays  can 
enter  the  eye. 

The  opera  glass  consists  of  two  Galilean  telescopes  placed  near  to- 
gether, so  as  to  produce  an  image  in  each  eye.  The  magnifying 
power  is  low,  seldom  exceeding  two  or  three  diameters.  Field  and 
night  glasses  are  simply  large  opera  glasses. 

532.  Reflecting  telescopes  are  of  several  different  forms, 
which  take  their  names  from  their  inventors.  Herschel's 
telescope  consists  of  a  single  concave  reflector,  M,  and  an 


FIG.  245. 

eye  piece,  O.  The  reflector  is  so  inclined  to  the  axis  of 
the  tube,  that  the  image  of  the  star  is  formed  in  front 
of  the  eye  piece,  near  the  side  of  the  tube,  and  is  then 
magnified  by  the  convex  lens. 

In  Newton's  telescope,  the  reflected  rays  are  received  on  a  small 
I ilano  mirror,  placed  in  the  axis  of  the  concave  mirror,  which  again 
reflects  them  to  an  eye  piece  attached  to  the  side  of  the  telescope.  Lord 
Rosse's  telescope  has  a  mirror  six  feet  in  diameter,  whose  focal  length 
is  lifty-four  feet.  The  amount  of  available  light  received  at  the  eye 
piece  exceeds  two  hundred  and  fifty  thousand  times  as  much  light  as 
commonly  enters  the  eye.  This  enormous  illuminating  power  enables 
the  observer  to  use  eye  glasses  whose  magnifying  power  is  so  great 
that  an  object  ;u>  large  as  the  capitol  at  Washington  could  readily  be 
perceived  at  the  distance  of  our  moon.  Its  highest  magnifying 
power  is  over  six  thousand  diameters. 


DOUBLE  REFRACTION.  297 

534.  Recapitulation. 

f  Sclerotic. 
Enveloping  coats  -I  Choroid. 

The  human  eye  consists  of  \  Retina. 

r  Aqueous  humor. 

Refracting  bodies  -I  Crystalline  lens. 
v  Vitreous  humor. 

The  sensation  of  sight  is  produced  by  luminous  undulations  passing 
through  (1.)  the  cornea,  (2.)  aqueous  humor,  (3.)  pupil,  (4.)  crystal- 
line lens,  (5.)  vitreous  humor,  to  the  retina,  and  there  exciting,  in  the 
layer  of  rods  and  cones,  vibrations,  which  are  conveyed  by  the  optic 
nerve  fibers  to  the  brain. 

The  ordinary  defects  of  the  eye  are 

f  Myopia. 

1.  Anomalies  of  refraction -I  Hypermetropia. 

v  Astigmatism. 

2.  Loss  of  power  of  accommodation Presbyopia. 

All  optical  instruments  are  combinations  of  either  prisms,  lenses, 
or  mirrors. 

DOUBLE  REFRACTION  AND  POLARIZATION. 

535.  If  a  crystal  of  Iceland  spar  be  placed  upon  an  ob- 
ject, as  in  Fig.  246,  a  double  image  will  be  perceived.  This 


phenomenon  is  called  double  refraction.  Most  transparent 
crystals  have  the  same  property  of  refracting  light  in  two 
separate  pencils.  The  manner  in  which  the  incident  ray  is 
divided  is  shown  in  Fig.  247.  Let  a  a;  be  a  line  joining  the 


298  NATURAL   PHILOSOPHY. 

obtuse  angles  of  a  crystal  of  Iceland  spar.  It  is  called  the 
axis  of  farm,  and  any  plane,  as  adxc,  parallel  to  this  axis 
and  perpendicular  to  any  face  o'f  the  crystal,  is  called  the 
plane  of  principal  section. 

Now,  suppose  a  ray  of  light  to  proceed  from 
a  dot  at  i;  it  will  be  refracted  in  two  rays,  tV, 
ief ',  and  will  give  two  images  of  equal  inten- 
sity, one  at  o  the  other  at  e.  The  first  of 
these  rays,  io',  has  a  constant  index  of  re- 
fraction 1.05,  and  is  governed  by  the  laws 
of  single  refraction.  It  is,  therefore,  called 
the  ordinary  ray.  The  other  ray,  ie/)  is  called 
the  extraordinary  ray. 

536.  There   is  one   direction  in  which  the  images  coin- 
cide   and    the    object   appears    single.      This    direction    is 
parallel  to  the  axis  of  form,  and  is  known  as  the  optic  axis 
of   the    crystal.      The    amount    of   separation   of  the   two 
images  will  be  the  greatest  when  the  direction  of  the  inci- 
dent ray  is  at  right  angles  to  the  optic  axis.     If  the  eye  be 
placed   directly  above  the  dot,  and  the   crystal   be  slowly 
turned  around,  the  ordinary  image  will  remain   stationary, 
while  the  extraordinary  will  revolve  about  it  at  varying  dis- 
tances.    Hence,  the  extraordinary  ray  has  a  variable  index 
of  refraction,  and  does  not,  in   general,  coincide  with   the 
plane  of  the  incident  ray. 

Crystals  with  but  one  axis  are  called  uniaxal,  as  Iceland 
spar,  tourmaline,  sapphire,  quartz.  Most  crystals  are  bi- 
axal;  that  is,  they  have  two  directions  in  which  the  image 
is  single,  as  sugar,  strontianite. 

537.  Both  the   ordinary   and  extraordinary  rays    have 
acquired   properties    which    distinguish    them   from    rays  re- 
ceived directly  from  the  sun  or  any  self-luminous  body,  ami 
are  said  to  be  polarized.     Li^ht    may  also  be  polarized  by 
single   n-iVaction,   reflection,  and   absorption.      A    body  capa- 
ble of  polari/in--  li'jht   is  called  a  /W</,/ 

The  difference  between  common  and  polari/.c<]  light  may  be  readily 
>hown.  Suppose  a  brain  of  -ohr  light  io  have  been  transmitted 
through  a  doubly  refracting  crystal,  ar,  and  one  of  the 


POLARIZATION. 


299 


FIG.  248. 


rays  to  be  cut  off  by  a  screen,  S.  If  the  ordinary  ray  be  allowed  to 
pass  through  a  second  crystal,  a'  z',  it  will  in  general  be  separated 
into  two  rays,  one  ordinary,  i'tX,  and  the  other  extraordinary,  iV,  but 
of  unequal  intensities. 

If  the  second  crystal,  which  is  called  an 
analyzer,  be  turned  around  until  the  two 
principal  planes  coincide,  that  is,  until  their 
axes  make  an  angle  of  0°  or  180°,  the  ex- 
traordinary ray  disappears,  and  the  ordi- 
nary has  its  greatest  intensity.  On  turning 
the  analyzer  farther  around,  the  ordinary 
ray  gradually  decreases  in  intensity,  while 
the  extraordinary  ray  re-appears  and  in- 
creases in  intensity.  When  the  principal 
planes  are  at  right  angles  to  each  other, 

that  is,  when  their  axes  have  been  turned  90°  or  270°,  the  ordinary 
ray  disappears,  and  the  extraordinary  ray  has  its  greatest  intensity. 

If  the  screen  be  moved  so  as  to  cut  off  the  ordinary  ray  and  allow 
the  extraordinary  to  fall  on  the  analyzer,  the  extraordinary  ray 
alone  will  be  transmitted  when  the  principal  planes  coincide,  and 
only  the  ordinary  when  the  principal  planes  are  at  right  angles.  At 
intermediate  positions,  the  refraction  is  double,  but  of  unequal  in- 
tensity, except  at  the  middle  point  of  each  quadrant. 

538.  Explanation  of  polarization.  If  we  regard  the 
waves  of  light  to  be  those  of  crests  and  hollows  (893),  the 
vibrations  will  be  transverse  to  the  direction  of  propagation. 
Now,  since  common  light  will  be  equally  transmitted  in  every 
conceivable  direction,  the  transverse  vibrations  must  take 
place  in  every  possible  plane. 

This  can  not  be  the  case  with  polarized  light,  since  its 
intensity  varies  from  a  maximum  to  zero  as  its  direction  to 
the  medium  which  it  encounters  varies.  It  has,  therefore, 
acquired  sides ;  that  is,  its  transverse  vibrations  may  be 
regarded  as  moving  in  a  single  plane,  as  east  and  west,  or 
up  and  down,  or  right  and  left.  Hence,  polarized  light 
consists  of  a  system  of  vibrations 
moving  in  a  single  plane  or  in 
parallel  planes. 

If,  then,  the  adjoining  figures  repre- 
sent sections  of  two  beams  of  light,  the 


/ 


FIG.  249. 


FIG.  250. 


300  NATURAL   PHILOSOPHY. 

radii  of  Fig.  249  will  represent  the  transverse  vibrations  of  common 

light,  and  the  parallel  lines  of  Fig.  250,  the  transverse  vibrations  of 

polarized  light. 

Now,  on  the  principle  of  the  resolution  of  forces,  polarized  light  may 

be  considered  as  moving  in  a  single   plane,   and   common   light  as 

equivalent  to  a  system  of  vibrations,  moving  in  two  planes  at  right 

angles  to  each  other.  Fig.  251.  When 
the  beam  is  polarized,  the  light  is  sepa- 
rated into  two  sets  of  vibrations,  which 
move  in  planes  at  right  angles  to  each 
other. 
In  the  case  of  the  Iceland  spar,  the  ordinary  ray  is  polarized  in  a 

plane  parallel  to  the  optic  axis,  and  the  extraordinary  ray  in  a  plane 

at  right  angles  to  that  axis. 

539.  Polarization  by  absorption.  If  a  crystal  of  tour- 
maline be  split  into  plates  parallel  with  its  axis,  these  plates 
will  be  doubly  refracting,  like  Iceland  spar.  They  also 
possess  the  property  of  rapidly  absorbing  the  ordinary  ray ; 
and  hence,  if  a  beam  of  solar  light  fall  upon  a  plate  of 
requisite  thickness,  only  the  extraordinary  ray  will  emerge. 
For  this  reason,  a  plate  of  tourmaline  is  a  convenient  means 
for  polarizing  light,  and  also  for  analyzing  light  that  has 
been  polarized  by  other  means. 

The  tourmaline  pincette  consists  of  two  such  plates  set 
in  movable  disks,  a  and  6,  Fig.  252.  If  either  plate  be  held 

between  the  eye  and  a 
candle,  the  light  will 
be  transmitted  polar- 
ized in  all  positions  of 
.  2:>2.  the  disk,  (but  colored 

by  the  accidental   tint 

of  the  crystal.)  If  the  two  disks  are  placed  in  front  of  each 
•  it IKT,  with  their  axes  parallel,  little  cliaiiLre  will  !»<•  observed; 
but  if  the  second  or  analyzing  plate  be  slowly  turned,  the 
liirht  will  gradually  become  more  feeble,  and  will  entirely 
ili-apprnr  when  the  plate  has  been  turned  1)0°. 

The  effect  of  the  tourmaline  is  analogous  to  that  of  two  gratings 
with  parallel  bars.  Fi.ir.  -•').'!•  If  a  card-board  model  of  a  wave  of 


POLARIZATION  BY  REFLECTION. 


301 


FIG.  253. 


li.«,'ht  be  presented  to  the  grating,  A,  only  the  vertical  portion  will  be 

permitted  to  pass.     When  this  portion,  which  represents  a  polarized 

wave,  reaches  C,   it   will   be 

stopped  if  the  gratings  at  C 

are  at  right  angles  to  A,  but 

will  pass  freely  if  C  be  turned 

a  quarter  round. 

If  either  ray  which 
has  been  polarized  by 
transmission  through  Ice- 
land spar  be  examined  by  a  tourmaline  analyzer,  it  will  be 
found  that  in  certain  positions  of  the  analyzer  all  the  light 
will  be  absorbed,  but  if  the  analyzer  be  turned  90°,  all  the 
light  will  be  transmitted.  The  ordinary  ray  will  be  trans- 
mitted where  the  extraordinary  was  absorbed,  and  absorbed 
where  the  other  was  transmitted. 

540.  Polarization  by  reflection.  When  light  falls  upon 
the  surface  of  any  transparent  medium,  the  reflected  ray  is 
more  or  less  polarized.  Let  AB,  Fig.  254,  be  a  plate  of 


R' 


FIG.  254. 


FIG.  255. 


glass,  and  I C  the  incident  ray.  A  small  portion  of  the 
light  will  be  reflected  at  each  surface,  in  the  direction,  C  R, 
ER',  and  the  remainder  transmitted.  All  the  reflected 
light  will  be  polarized  when  the  angle  of  incidence  is  such 
that  the  reflected  and  refracted  rays  are  at  right  angles  to 
each  other.  This  is  called  the  polarizing  angle.  The  polar- 
izing angle  for  glass  is  54°  35',  for  water  52°  45'.  * 

*  The  angle  of  polarization  for  light  passing  from  air  into  a  denser 
medium  is  such  that  the  tangent  of  the  incident  ray,  which  is  reflected 
polarized,  is  equal  to  the  index  of  refraction  for  the  reflecting  medium. 


302  NATURAL    PHILOSOPHY. 

If  the  polarized  ray  tall  upon  a  second  plate  at  an  equal  angle, 
vix.:  ">4°  ;>"/,  it  will  lie  entirely  reflected  when  the  two  plates  are 
parallel,  but  if  the  upper  plate  be  turned  around  this  ray  as  an  axis, 
so  as  to  maintain  the  same  angle  of  incidence,  the  ray  will  gradually 
decrease  in  intensity,  and  will  entirely  disappear  when  the  two  plates 
are  at  right  angles  to  each  other.  Fig.  255. 

If  the  polarized  ray  be  examined  by  an  analyzer  of  Iceland  spar, 
it  will  be  refracted  singly  and  ordinarily  when  the  principal  plane 
coincides  with  the  plane  of  reflection ;  singly  and  extraordinarily, 
when  the  principal  plane  is  at  right  angles  to  the  plane  of  reflection, 
and  in  all  other  cases  will  be  separated  into  two  pencils  which  are,  in 
general,  of  unequal  intensity. 

541.  Polarization  by  refraction.     When  light  is  polar- 
ized by  reflection  from  the  surface  of  a  transparent  medium 
an  equal  amount  of  the  transmitted  ray,  E  D,  is  polarized 
by  refraction.      But  as  the  amount  of  light  transmitted  is 
much  greater  than   that  reflected,  only  a  small  portion  of 
the   transmitted    ray   will    be    polarized,    and   will    emerge 
mixed  with  common  light.     If,  however,  several  plates  of 
glass  or  mica  be  laid  one  upon   another,  the   light  will  be 
partially  polarized  at  each  refraction,   and   if  eighteen  or 
twenty  plates  be  used,  very  nearly  all  of  the   transmitted 
light  will  be  polarized. 

If  light,  polarized  by  refraction,  fall  upon  a  glass  plate  at  its  polar- 
izing angle,  it  will  be  wholly  reflected  when  the  surface  is  at  right 
angles  to  the  plane  of  refraction,  and  wholly  transmitted  when  the 
reflecting  surface  is  turned  90°.  Therefore,  the  planes  of  polarization 
by  refract i< m  and  reflection  are  at  right  uncles  to  each  other. 

If  examined  by  an  analyzer  of  tourmaline,  or  of  Iceland  spar,  the 
reflected  ray  will  be  transmitted  where  the  refracted  ray  is  stopped, 
and  stopped  where  the  refracted  ray  is  transmitted. 

542.  Rays  of  light,  polarized  in  the  same  plane,  may  be 
made   to   interfere  with   each  other  in   the  same  manner  as 
rays  of  common  light.     The  chromatic  effects  produced  are 
exceedingly  striking  and  beautiful. 

The  simplest  manner  of  producing  these  effects  is  by  in- 
terposing a  thin  plate  <>{'  any  doubly  refraetiu«:  substance 
IK  t ween  the  polarizer  ami  analv/.er.  Thus,  if  a  thin  film 
of  Iceland  spar  be  placed  IM-IWM-II  the  disks  ..fa  tourmaline 


R  0  TA  TOR  Y  POL  ARIZ  A  TION. 


303 


Fio.  256. 


FIG.  257. 


pincette,  with  the  axes  of  the  tourmalines  perpendicular,  a 
beautiful  series  of  colored  rings  traversed  by  a  black  cross 
be  seen.  Fig.  256.  If  the  analyzer  be  turned,  the 

colors    will   gradually 

change,  and  when  the 

axes-  are  parallel,  the 

tints  will   be  comple- 
mentary to    the    first 

series,  and   the  cross 

will     become     white. 

Fig.  257.     Any  uni- 

axal  crystal  will  pro- 
duce similar  effects.    Biaxal  crystals  produce  double  systems 
of  rings,  with  most  curious  and  characteristic  combinations. 

543.  Many  other  substances,  as  slices  of  quills,  parings 
of  horses'  hoofs,  grains  of  starch,  compressed  glass,  gums, 
and  jellies,    will,    under   like    circumstances,    give    similar 
colors  and  rings,  and  thereby  indicate  a  doubly  refracting 
structure.      Whenever   there   is   the    least   tendency  to   an 
axial  arrangement  in  the  molecular  structure  of  transparent 
bodies,  it  may  be  determined,  at  least  in  part,  by  transmit- 
ting through  the  body  a  polarized  ray. 

If  polarized  light  be  transmitted  through  unannealed  glass,  irregu- 
larly heated,  compressed,  or  bent,  the  amount  of  molecular  change 
in  the  glass  caused  by  the  disturbing  force  may  be  at  once  indicated 
and  measured  by  the  colors  displayed,  by  viewing  the  transmitted 
ray  through  an  analyzer. 

544.  Rotatory  polarization.     If  two  tourmaline  plates  be 
crossed,  no  light  will  be  transmitted.     If,  now,  a  section  of 
quartz  crystal,  cut  at  right  angles  to  the  axis,  be  placed 
between  the  polarizer  and  analyzer,  more  or  less  light  will 
be  transmitted,  and  to  extinguish  it,  the  analyzer  must  be 
turned  through  a  certain  angle.     This  phenomenon  is  called 
rotatory  polarization. 

Some  kinds  of  quartz  turn  the  plane  of  polarization   to 
the  right  hand  and  others  to  the  left,  and  the  crystals  are 


304  NATURAL    PHILOSOPHY. 

termed  right  handed  or  left  handed,  according  to  the  effect 
produced.  The  action  of  the  plate  is  proportioned  to  its 
thickness,  and  is  more  energetic  the  greater  the  refrangi- 
bility  of  the  ray.  Thus,  for  a  plate  of  quartz  one  twenty- 
fifth  of  an  inch  thick,  a  ray  of  red  light  requires  the  analyzer 
to  be  turned  17°,  and  a  ray  of  violet  light,  44°.  If  white 
light  be  used,  the  same  crystal  will  give  different  colors  as 
the  analyzer  is  turned. 

545.  Certain  liquids  also  possess  the  property  of  rotatory 
polarization.  Thus,  solutions  of  cane  sugar,  and  oil  of 
lemons,  give  a  right-handed  rotation;  albumen,  and  solu- 
tions of  uncrystallizable  sugar,  give  a  left-handed  rotation. 

Hence,  if  a  ray  of  polarized  light  be  transmitted  through  a  sirup 
of  pure  cane  sugar,  the  strength  of  the  sirup  may  be  determined  by 
the  angle  through  which  the  analyzer  must  be  turned  to  produce  the 
violet  tint.  A  mixture  of  two  liquids,  acting  oppositely,  will  pro- 
duce a  result  equal  to  the  difference  between  the  two;  hence,  a  simi- 
lar contrivance  may  be  used  to  determine  the  proportion  of  cane 
and  fruit  sugars  in  a  sirup,  or  to  determine  the  adulteration  of 
various  essential  oils. 

Other  uses  of  polarized  light.  By  viewing  the  heavenly 
bodies  through  an  analyzer,  Arago  was  enabled  to  decide 
that  the  moon  and  planets  shine  by  reflected  light,  because 
much  of  their  light  is  polarized.  On  the  other  hand,  the 
fixed  stars  are  self  luminous,  because  their  light  is  unpo- 
larized. 

Polarized  light  is  of  great  value  in  microscopic  investi- 
gations, because,  by  means  of  characteristic  rings  and 
axial  lines,  various  bodies  may  be  detected  in  very  minute 
<|ii:uitities.  Thus,  the  various  kinds  of  starch  give  charac- 
teristic bands  which  serve  to  distinguish  one  from  the  other. 

546.  Recapitulation. 

fl>ouhlr  refraction. 
Onlinarv   rHYartion. 
— a-— j       i .' ;   Reflection. 

Absorption. 


HE  A  T. 


305 


CHAPTER   VIII. 


FYRONOMICS. 

547.  The  sensations  of  warmth  and  cold  are  due  to  the 
action  of  a  force  which  every  one  recognizes  as  heat.     These 
tt -rms  are,  however,  merely  relative,  as  the  same  substance 
may  at  the  same  time  appear  warm  to  one  individual  and 
cold  to  another.     If  we  place  the  right  hand  in  iced  water 
and  the  left  in  hot,   and   then  suddenly  transfer  both   to 
ordinary  cistern  water,  the  sensations  of  either  hand  will 
be  reversed.     Our  sensations,   therefore,   can  not  be  used 
as  a  means  of  measuring  heat  accurately.     We  may  accom- 
plish this   result  by  means  of  the  effect  of  heat  on  bodies 
not  endowed  with  sensation. 

548.  The  first   effect  of  heat  on  any  body,  solid,  liquid, 
or  aeriform,  is  to  expand  it. 

The  expansion  of  gases  may  be  readily  shown 
by  the  air  thermometer.  Fig.  258.  This  consists 
simply  of  a  bulb  of  glass,  with  a  long  narrow 
stem,  dipping  into  colored  water.  If  the  bulb  be 
warmed  by  the  hand,  the  air  within  will  so  ex- 
pand that  a  portion  will  be  expelled  and  rise  in 
bubbles  through  the  liquid.  On  cooling,  the  por- 
tion of  air  remaining  will  contract  to  its  former 
volume,  and  the  water  will  take  the  place  of  the 
air  expelled. 

The  experiment  may  then  be  continued  indefi- 
nitely. The  expansion  and  contraction  may  be 
measured  by  the  scale  attached  to  the  stem.  If 
other  gases  than  air  are  used  to  fill  the  stem,  it 
will  be  found  that  all  expand  equally  and  regu- 
larly for  successive  increments  of  heat.  Fio.  258. 

The  expansion  of  liquids  may  be  shown  by  a  flask,  hav- 
ing a  long  narrow  tube  fitted  to  its  neck  by  a  cork.  Fig. 
259. 

N.  P.  20. 


306 


NATURAL  FHILOSOrilY. 


FIG.  259. 


If  the  flask  be  filled  with  alcohol  and  plunged  in 
boiling  water,  the  expansion  of  the  alcohol  will  be 
manifested  by  its  rise  in  the  tube.  If  other  liquids  are 
used  to  fill  the  flask,  most  of  them  will  expand  less 
than  the  alcohol,  showing  that  different  liquids  expand 
unequally  for  the  same  increments  of  heat. 

A  scale  attached  to  the 
tube  will  convert  the  appa- 
ratiH  into  a  thermometer, 
which  may  be  termed  mer- 
curial, alcoholic,  water,  etc., 
according  to  the  liquid  used. 

The  expansion  of  solids  may  be 
shown  by  a  Gravesande's  ring.  Fig. 
260. 

A  brass  ball  is  so  made  that,  at  ordi- 
nary temperatures,  it  passes  freely  through 
the  ring,  ra.  When  the  ball  is  heated,  it 
expands,  and  will  no  longer  pass  through 
the  ring.  FIG.  260. 

The  preceding  experiments  show  an  "increase  in  volume 
which  is  termed  cubical  expansion.  In  solids  the  expansion 
is  sometimes  measured  in  one  direction  only,  and  is  then 
termed  linear  expansion. 

The  pyrometer,  Fig.  261,  may  be  used  to  show  the  linear 
expansion  of  solids. 

A  metallic  rod,  A,  fixed   at  one  end,  B,  presses  at  the  other  end 


FIG.  2fii. 


the  short  arm  of  tin-  indrx,   K.      When  tin-  rod   is  lira  ted,  it 

and   drives  the  index   along   the   scale.     By  using   rods  of  different 


EXPANSION   BY  HEAT.  307 

substances,  it  will  be  seen  that  different  solids  expand  unequally  for 
equal  increments  of  heat. 

549.  The  unequal  expansion  of  different  metals  is  well 
shown  by  a  compound  bar,  made  by  riveting  together  two 
bars  of  iron  and  brass,  at  different  points  along  their  whole 
length,  as  shown  in  Fig.  262. 

If  the  bar  is  straight  at  ordinary  temperature,  it  will  so  bend 
when  hot  water  is  poured  on  it  that  the  brass  will  be  on  the  convex 


FIG.  262.  FIG.  263. 

side  of  the  curve,  and  bend  in  the  opposite  direction  when  cold  water 
is  poured  on  it.  The  brass  expands  and  contracts  more  than  the  iron, 
and  the  bar  curves  to  accommodate  the  inequality  of  the  length  which 
results.  This  principle  has  been  applied  to  the  construction  of  metallic 
thermometers. 

Clay  does  not  expand  by  heat,  but  contracts  permanently,  by 
reason  of  chemical  changes  among  its  particles.  In  the  experiments 
detailed,  the  bodies  will  be  found  to  contract  on  cooling,  and  assume 
their  original  volume,  as  soon  as  they  attain  their  former  tempera- 
ture. Certain  metals,  as  lead  and  zinc,  are  exceptions  to  this  law  of 
cooling,  the  contraction  being  at  each  time  a  little  less  than  the  ex- 
pansion. 

550.  From  these  experiments  it  is  evident  (1.)  that  the 
volume  of  all  bodies  is  increased  by  heat;  (2.)  that  this  in- 
crease of  volume  is  due  to  motion  among  the  molecules  of 
the  bodies,  which  tends  continually  to  separate  them;  (3.) 
that  the  intensity  of  the  heat  may  be  measured  by  the 
degree  of  the  molecular  motion.  From  these  and  other 
considerations,  to  be  detailed  hereafter,  it  is  assumed  that 

Heat  is  that  mode  of  molecular  motion  which  may  be  meas- 
ured by  the  expansion  of  bodie*. 

By  this  definition  it  is  understood  (1.)  that  the  molecules 
of  every  body  are  in  continual  motion;  (2.)  that  when  this 
motion  increases  in  intensity,  the  body  becomes  warmer; 
(3.)  that  when  this  motion  decreases  in  intensity,  the  body 
becomes  cooler.  An  older  theory,  which  regarded  heat  as 


308  NATURAL   PHILOSOPHY. 

imponderable  matter,  has  been  generally  discarded  while 
some  of  its  terms  have  been  retained :  hence,  the  student 
must  remember  that  when  heat  is  described  as  passing  from 
one  body  to  another,  it  means  that  the  molecular  motion 
of  one  body  is  communicated  to  the  molecules  of  another, 
and  not  that  any  material  agent  has  passed. 

551.  Temperature  is  the  intensity  of  heat  referred  to 
some  arbitrary  standard.  The  standards  assumed  are  those 
of  melting  ice  and  of  water  boiling  under  the  pressure  of 
one  atmosphere,  which  are  found  by  experiment  to  represent 
invariable  temperatures.  These  temperatures  are  called, 
severally,  the  freezing  and  the  boiling  points. 

0  A  tJiermometer  is  an  instrument  which  measures 
temperatures.  Thermometers  may  be  formed  of 
•212  anv  substance  in  which  the  expansion  on  heating 
and  the  corresponding  contraction  on  cooling  may 
be  determined.  The  mercurial  thermometer  con- 
sists of  a  capillary  glass  tube,  at  one  end  of  which 
is  blown  a  bulb;  the  bulb  and  part  of  the  tube 
are  filled  with  mercury. 

The  mercury  and  the  glass  are  both  affected  by 
heat,  but,  under  the  same  circumstances,  the  mer- 
cury expands  or  contracts  seven  times  as  much  as 
the  glass.     Therefore,  if  the  instrument  is  warmed 
the   mercury  will   rise  in   the  tube;   and   if  it  is 
Fi.i.264.      cooled,  the  mercury  will  sink  in   the  tube.     For 
the   purpose  of  comparing   one   instrument  with 
another,  arbitrary  scales   have  been  devised,  by  which   the 
variation  in  the  mercurial  column  may  be  designated. 

The  fVee/.iiiLr  and  boiling  points  are  first  determined  by  im- 
mersing the  instrument  in  melting  ice  and  in  boiling  water, 
and  the  height  <>f  the  column  in  each  case  is  marked  on 
the  tube  or  on  the  scale  attached  to  it.  These  points  being 
determined,  the  interval  between  them  is  then  divided  into 
any  number  of  equal  parts  called  degrees,  and  parts  of  the 


THERUOMETRIC  SCALES. 


309 


same  length  are   set  off  above  and  below  the  boiling  and 
freezing  points,  as  far  as  may  be  required. 

552.  Fahrenheit's  scale  is  in  common  use  in  this  country. 
It  marks   the  boiling  point  by  212°  and  the  freezing  point 
by  32°.     The  zero,  or  0°,  of  this  scale  was  determined  by 
a  mixture  of  ice  and  salt. 

The  scale  used  in  France,  and  generally  employed  in 
scientific  researches,  is  the  centigrade,  invented  by  Celsius. 
It  marks  the  freezing  point  by  0°,  and  the  boiling  by  100°. 

Reaumur's  scale,  which  is  used  in  Germany  and  Spain, 
marks  the  freezing  point  by  0°,  and  the  boiling  by  80°. 

These  scales  are  distinguished  from  each  other  by  the  letters  F., 
C.,  and  R.  The  divisions  below  zero  are  indicated  by  the  negative 
sign;  thus,  —10°  signifies  ten  degrees  below  zero;  +  10°,  or  10°  sig- 
nifies ten  degrees  above  zero.  The  interval  between  the  freezing  and 
boiling  points  is,  therefore,  divided  by  Fahrenheit  into  180°,  by  Celsius 
into  100°,  and  by  Reaumur  into  80° ;  hence,  180°  F  =  100°  C  =  80°  R, 
or  l0F  =  f°C  =  f°R. 

Bearing  in  mind  that  Fahrenheit's  zero  is  32°  below  the  freezing 
point,  one  scale  may  readily  be  converted  into  another,  thus: 

F  =  fC  +  32  =  fR  +  32. 
C  =  (F  —  32)  f  r=  f  R> 
R  =  (F  —  32)  f  =  |  C. 

All  these  scales  are  alike  arbitrary;  but 
undoubtedly  the  most  rational  and  conven- 
ient is  the  centigrade. 

553.  As  mercury  freezes  at  — 37°. 9 
F.,  and  boils  at  662°  F.,  it  can  not 
be  used  to  measure  temperatures  be- 
yond these  limits.    Thermometers  filled 
with  alcohol  are  used  to  measure  ex- 
treme   cold,    and    various    forms    of 
metallic    thermometers    are    used    to 
measure    extreme    heat.      The    pyro- 
meter, Fig.  261  is  an  example.     The 

air  thermometer,  Fig.  258,  is  very  sensible  to  changes  in  tem- 
perature, but  is  affected  also  by  changes  in  the  atmosphere. 


FIG.  265. 


310  NATURAL  PHILOSOPHY. 

Regnault  has  devised  an  air  thermometer  which  is  by  far 
the  most  reliable  thermometer  known.  It  is  very  sensitive 
and  may  be  used  for  any  temperature,  but  is  too  compli- 
cated for  ordinary  use. 

The  differential  thermometer,  Fig.  265,  has  two  closed 
bulbs  filled  with  air  and  connected  by  a  U  tube,  containing 
a  little  sulphuric  acid.  It  indicates  only  the  difference  in  tem- 
perature of  the  two  bulbs ;  if  one  is  warmer  than  the  other, 
the  liquid  in  the  tube  will  be  forced  toward  the  colder  bulb. 

For  very  delicate  investigations,  the  thermo-multiplier, 
described  in  (771),  is  now  universally  employed. 

554.  The  coefficient  of  expansion  is  the  small  fraction 
which  measures  the  expansion  of  a  body  on  being  raised 
from  the  freezing  point  to  one  degree  above.  The  rate  of 
expansion  for  all  gases  is  very  nearly  the  same,  being 
49*  9  of  their  bulk  for  each  degree  Fahrenheit,  or  -%fa  of 
their  bulk  for  each  degree  centigrade.  The  rate  of  expan- 
sion for  solids  and  liquids  increases  as  the  temperature  rises. 
Between  32°  F.  and  212°  F.  this  increase  in  rate  is  hardly  ap- 
preciable, so  that  the  coefficient  of  expansion  will  very  nearly 
represent  the  expansion  of  each  degree.  For  higher  temper- 
atures, the  increase  in  rate  forms  a  considerable  quantity. 

For  this  reason  all  thermometers  should  be  graduated  by 
comparison  with  Regnault's  air  thermometer.  Thus,  the  tem- 
perature of  572° F.,  as  measured  by  Regnault's  thermometer, 
would  be  indicated  by  586°  F.  if  measured  by  an  ordinary 
mercurial  thermometer,  because  of  the  increase  in  the  rate  of 
expansion  in  mercury,  as  the  temperature  rises.  Alcoholic 
thermometers  are  even  less  reliable,  because  the  expansion 
of  alcohol  at  all  temperatures  is  exceedingly  irregular. 

If  a  rod,  whose  length  is  taken  as  unity,  have  a  coefficient  of  ex- 
pansion n-jin -nitr.l  I iv  '(  ,  then  its  total  Imirih  after  being  heated  one 
degree  will  be  1  -f  .  If  the  same  substance  be  in  the  form  of  a 
square,  the  superficial  contents,  after  heating  one  decree,  will  be 
(l  -f-l)2=l  -f  l+#.  Finally,  if  the  same  substance  be  in  the 


EXPANSION.  311 

form  of  a  cube,  the  volume,  on  being  raised  one  degree,  will  be 
(l  +|)3  =  l-r  £  + Jj+^r.  Now,  as  |  is  a  very  small  quantity, 
its  powers,  55 ,  -3 ,  may  be  neglected ;  consequently,  the  superficial 
coefficient  of  expansion  is  nearly  twice,  and  the  cubical  coefficient 
three  times  the  linear  coefficient. 

Table  of  Expansion  from  32°  F.  to  212°  JF*. 


Solids.  Linear.      Cubical. 

Flintglass T^¥T  ^ 

Platinum 

Steel.... 


Brass 
Silver 
Tin 
Zinc 


Fluids.  Cubical. 

Mercury ^ 

Water 

The  fixed  oils Ty-§ 

Alcohol , £ 

Air  and  the  permanent  gases.  £f§ 


21 


555.  The  amount  of  force  exerted  in  expansion  or  con- 
traction is  enormous ;  for  it  is  equal  to  that  which  would 
be  required  to  stretch  or  compress  the  material  to  the  same 
extent  by  mechanical  means. 

Water,  at  the  temperature  of  128°  F.,  is  compressed  .000044  of  its 
volume  by  the  pressure  of  one  atmosphere.  On  being  heated  from 
32°  F.,  to  212°  F.,  it  expands  .0466  of  its  volume.  Therefore,  to  re- 
store boiling  water  to  its  bulk  at  freezing  would  require  a  pressure  of 
over  one  thousand  atmospheres.  The  expansive  force  of  water  for 
each  degree  F.  is  nearly  ninety  pounds  per  square  inch.  Hence,  if 
a  closed  vessel  be  completely  filled  with  cold  water,  it  must  speedily 
burst  when  heat  is  applied. 

A  bar  of  wrought  iron  expands,  for  each  degree  F.,  with  a  force 
of  nearly  two  hundred  pounds  to  the  square  inch.  This  force  had  a 
curious  application  in  the  Museum  of  Arts  and  Trades,  in  Paris. 
The  walls  of  an  arched  gallery  had  bulged  outward  by  the  weight 
of  the  arch.  Iron  bars  were  placed  across  the  building  and  screwed 
into  plates  on  the  outside.  The  alternate  bars  were  then  heated,  and 
as  soon  as  they  had  expanded  the  plates  were  screwed  up  tightly  to 
the  walls.  As  the  bars  cooled  and  contracted,  they  drew  the  walls 
closer  together.  The  operation  was  repeated  until  the  walls  had 
attained  the  vertical  position. 


312  NATURAL   PHILOSOPHY. 

On  the  same  principle  tires  are  fastened  on  wheels.  The  tire, 
made  a  little  smaller  than  the  wheel,  is  heated  red  hot,  and  while 
expanded  is  placed  in  position.  On  cooling,  it  not  only  secures  itself 
on  the  rim,  but  holds  all  the  other  parts  of  the  wheel  in  position. 

It  is  often  necessary  to  take  into  account  the  changes  of  length 
produced  by  heat.  In  railways,  a  small  interval  must  be  left  between 
the  ends  of  the  iron  rails.  Iron  bars  built  into  masonry  should  be 
left  free  at  one  end. 

Brittle  substances,  as  glass  and  cast  iron,  often  crack  on  being 
heated  suddenly ;  because  the  outside  is  heated  sooner  than  the  inside, 
and  thereby  causes  an  unequal  expansion.  A  sudden  cooling,  by  in- 
ducing unequal  contraction,  has  the  same  effect.  The  thicker  the 
plate  the  greater  the  liability  to  fracture. 

556.  Water  presents  a  singular  exception  to  the  general 
law  of  expansion  and  contraction  by  heat.     If  a  flask,  with 
a  long  and  very  slender  neck,  Fig.  259,  be  filled  with  boiling 
water  and  allowed  to  cool,  the  water  will  go  on  contracting, 
though    irregularly,    until   it   reaches    the    temperature    of 
39°. 2  F.     It  then   begins  to   expand,  and  continues  to  do 
so  until   it  freezes.     At  32°  F.  it  occupies  the  same  space 
that  it  did  at   48°  F.     The   maximum   density  of  water  is 
consequently  attained  at  39°. 2  F.,  and  above  or  below  this 
temperature  it  expands. 

This  fact  is  of  infinite  importance  in  nature.  In  winter,  the  lakes 
and  rivers  cool  until  they  attain  their  maximum  density  throughout; 
if  the  cooling  proceeds  further,  expansion  begins  at  the  surface,  and 
the  lighter  though  colder  particles  float  upon  the  warmer  water  below. 
Hence,  the  freezing  takes  place  only  on  the  surface. 

At  the  moment  of  freezing,  the  water  undergoes  a  sudden  enlarge- 
ment, of  about  ten  per  cent,  in  volume,  in  becoming  ice.  The  ice 
once  formed  covers  the  water  like  a  blanket,  and  renders  the  fivr/ing 
process  v.-ry  -low.  If  the  ice  were  specifically  heavier  than  water, 
large  ma-.--  would  form  at  the  bottom  each  winter,  which  the  heat 
of  the  succeeding  snnmirr  would  be  unable  to  melt  entirely,  and  thus 
our  lakes  would  in  time  become  solid. 

SPECIFIC   HEAT. 

557.  The  temperature  of  a  body  affords  \\^  imliratimi  of 
the  amount  of  heat  it  rontuin.s.      The  /<TO  point  is  entirely 


SPECIFIC  HEAT.  313 

arbitrary,  and  does  not  indicate  the  absence  of  heat.  Bodies 
have  been  cooled  to  — 220°  F.  without  reaching  the  absolute 
zero,  or  the  point  at  which  molecular  motion  ceases.  It  is 
a  mistake,  therefore,  to  say  that  water  at  100°  is  twice  as 
hot  as  water  at  50°,  because  ratios  can  not  be  drawn  except 
from  an  absolute  zero.  It  is  impossible  to  measure  the  ab- 
solute amount  of  heat  gained  or  lost  by  a  body,  but  we  have 
a  measure  of  the  relative  amount  in  the  thermal  unit.  The 
tln-nnnl  unit  is  the  quantity  of  heat  required  to  raise  one 
pound  of  water  from  32°  F.  to  33°  F. 

558.  The  heat  lost  in  cooling  is  precisely  equivalent  to 
that  required  to  raise  the  same  body  through  the  same 
number  of  degrees.  Hence,  if  different  bodies  of  the  same 
weight  be  heated  to  the  same  temperature,  (say  212°  F.,) 
and  then  placed  on  cakes  of  ice,  the  amount  of  ice  melted 
will  be  in  proportion  to  the  number  of  thermal  units  they 
contain.  In  comparison  with  water,  sulphur  will  melt  -J-, 
iron  £,  mercury  -^  as  much  ice ;  consequently,  these  frac- 
tions will  express  the  relative  amount  of  heat  required  to 
raise  them  to  the  same  temperature.  The  heat  required  to 
raise  one  pound  of  any  substance  1°  F.,  compared  with  the 
thermal  unit,  is  the  specific  heat  of  the  substance.  The  spe- 
cific heat  of  water  is,  of  course,  1.00. 

Three  methods  of  measuring  specific  heat  are  in  use:  (1.) 
the  method  by  melting  ice,  just  mentioned;  (2.)  by  mix- 
tures; (3.)  by  cooling. 

The  method  by  mixture.  If  a  pound  of  water  at  212°  F. 
be  mixed  with  another  pound  at  32°  F.,  the  temperature 
of  the  mixture  will  be  &2±!^L2f  -  122° ;  one  pound  gains 
exactly  the  temperature  the  other  loses.  This  will  not  be 
the  case  if  dissimilar  substances  are  mixed  together.  If  a 
pound  of  mercury  at  212°  F.  be  mixed  with  a  pound  of 
water  at  32°  F.,  the  resulting  temperature  will  be  37°. 8  F. 
The  mercury  loses  174°. 2,  while  the  water  gains  5°. 8.  The 
specific  heat  of  mercury  is,  therefore,  yy^  =  .033. 


NATURAL   PHILOSOPHY. 

The  method  by  cooling.  If  two  thermometers  of  the  same 
volume  are  filled,  one  with  mercury  and  the  other  with 
water,  and  cooled  from  a  common  temperature,  the  mercu- 
rial thermometer  will  cool  more  than  twice  as  fast  as  the 
water  thermometer.  For  equal  volumes,  the  relative  heat 
of  mercury  is  ^4,  but  as  mercury  is  13.6  times  heavier  than 
water,  the  specific  heat  of  mercury  is,  as  before,  ^i  -=-  13.6 
= .033. 

Either  of  these  methods  may  be  employed  for  finding  the 
specific  heat  of  solids  and  liquids.  Proper  allowance  must 
always  be  made  for  the  heat  dissipated  in  the  apparatus 
employed. 

559.  The  specific  heat  of  aeriform  bodies  is  determined 
by  passing  a  current  of  heated  gas  through  a  coiled  metallic 
tube,  immersed  in  water,  and  noting  the  rise  of  tempera- 
ture produced  in  the  water  when  a  given  weight  of  the  gas 
has  been  cooled  a  known  temperature.  The  specific  heat  of 
equal  volumes  can  be  calculated  from  those  of  equal  weights 
by  multiplying  the  numbers  obtained  for  weights  by  the 
specific  gravity  of  each  gas. 

The  specific  heat  of  all  substances  except  the  permanent  gases  in- 
creases with  the  rise  of  temperature;  owing,  probably  to  the  expan- 
sion caused  by  heat.  A  substance  in  the  liquid  state  has  a  higher 
specific  heat  than  when  it  is  in  the  solid  or  aeriform  condition. 
Thus,  water  has  double  the  specific  heat  of  ice,  and  more  than  double 
the  specific  heat  of  steam.  These  facts  are  shown  by  the  annexed 
tables : 

Table  of  Mean  Specific  Heat. 

Betwi-i-n  Betwr-n 

32°  F.  iiml  -J1J    F.     '.'.'I    V.  iiii<l  .'.7-J     F. 

M.n-ury 0330  .0350 

Platinum  0335  .0355 

Silver 0557  .0611 

Copper ()!)!!»  .1013 

Iron 1098  .1218 

Glaaa 1770  .1900 


VA  P  ORIZA  TION.  315 

Specific  Heat  of  Gases  and  Vapors. 

Equal  volumes.  Equal  weights. 

Air 2375  .2375 

Oxygen 2405  .2175 

Hydrogen 2359  3.4090 

Ammonia  .. 2996  .5084 

Chloroform  6461  .1566 

Turpentine 2.3776  .5061 

Specific  Heat  of  the  same  substance  in  ^Different  States. 

Solid.  Liquid.  Aeriform. 

Water 5050  1.0000  .4805 

Phosphorus 1788  .2045  

Bromine 0843  .1060  .0555 

Lead  0314  .0482  

Alcohol .5050  .4534 

Ether .5467  .4797 

560.  With  the   exception  of  hydrogen,  water  possesses 
the  highest  specific  heat   known.     The   presence  of  large 
bodies  of  water  has,  for  this   reason,   a  decided  effect  in 
moderating  the  rapidity  of  transitions  from  hot  to  cold,  or 
from    cold    to    hot,    owing  to   the   large   quantity  of  heat 
which  seas  absorb  or  emit,  in   accommodating  themselves 
to  changes  in  external  temperatures.     An  oceanic  climate 
is,    therefore,    more    equable   than   an   inland   climate;    its 
summers  are  cooler  and   its   winters  warmer. 

On  the  islands  of  lake  Erie,  water  does  not  freeze  until  the  water 
of  the  lake  is  cooled  to  40°  F.,  thus  prolonging  the  season  sufficiently 
to  ripen  grapes.  A  daily  effect  is  witnessed  on  the  tropical  islands  in 
the  land  and  sea  breezes.  While  the  sun  shines,  the  land  becomes 
warmer  than  the  ocean,  and,  by  consequence,  the  air  above  the  land 
becomes  heated  and  rises,  and  cold  air  rushes  in  from  the  ocean, 
producing  a  sea  breeze;  in  the  night,  the  land  is  sooner  cooled,  the 
air  above  becomes  more  dense,  and  flows  out  toward  the  ocean  in  a 
land  bi-eeze. 

FUSION   AND    VAPORIZATION. 

561,  The  second  effect  of  heat  on  a  solid  is  to  change  its 
molecular   condition — to  melt  it.     Some  solids,  as  paper, 


316  NATURAL  PHILOSOPHY. 

wood,  and  wool,  do  not  melt,  but  are  decomposed.  The 
temperature  at  which  solids  melt  differs  for  different  sub- 
stances, but  is  invariable  for  the  same  substance,  if  the 
pressure  is  constant.  This  temperature  is  called  the  indtiiuj 
point. 

Table  of  Melting  *Poi)its,  in  degrees  Fahrenheit. 


Mercury —37.9 

Bromine -f    9.5 

Ice 32. 

Phosphorus  111.5 

Potassium 136. 

Tin ...  451 


Bismuth  512 

Lead 620 

Zinc 680 

Silver 1832 

Gold 2282 

Wrought  iron 2912 


Certain  bodies,  as  iron,  platinum,  glass,  and  wax,  soften 
and  become  plastic  before  they  fuse.  It  is  in  this  plastic 
state  that  glass  is  worked,  and  iron  or  platinum  forged. 
Bodies  difficult  of  fusion  are  termed  refractory:  such  are 
silica,  lime,  and  carbon. 

562.  The  melting  point  of  an  alloy  is  often  lower  than 
that  of  either  of  its  components.     Thus,  Rose's  metal,  consisting 
of  four  parts  of  bismuth,  one  of  lead,  and  one  of  tin,  fuses 
at  201°  F.     A  mixture  of  equivalent  parts  of  carbonate  of 
potassa  and  carbonate  of  soda,  melts  at  a  lower  temperature 
than   either  salt  separately.     Such   a  mixture  added  to  an 
ore  to  promote  the  formation  of  a  fusible  medium,  is  termed 
a  flux. 

563.  Freezing  point.     If  a  substance  in  a  liquid  form  is 
cooled    sufficiently,    it   generally   solidifies    at   the  melting 
point.     The    freezing    point    may    be    lowered    by  various 
means. 

Thus,  the  freezing  point  of  water  lias  been  lowered  by  pressure  to 
0°  F.  If  wait  r.  drjirivi-d  of  air,  i.>  allowed  to  cool  very  slowly, 
without  agitation,  it  may  be  cooled  to  10°  F.  bclcuv  it  fivc/rs.  When 
in  this  condition,  a  gentle  jolt,  or  tin-  addition  of  a  bit  of  ice,  will 
OHM  immediate  congelation,  and  the  temperature  will  suddenly  rise 


LATENT  HEAT.  317 

to  32°  F.  Tn  fine  capillary  tubes,  water  has  been  lowered  to  — 4°F. 
without  solidification.  This  fact  probably  explains  why  sap  is  not 
frozen  in  plants.  The  freezing  point  of  water  is  lowered  by  the 
fuvsi-nre  of  salts  in  solution.  Sea  water  freezes  at  27°.4  F.  Saturated 
brine  freezes  at  — 4°  F. 

In  such  cases  nearly  pure  ice  is  formed  by  freezing.  The  water 
appi-ars  to  crystallize  out,  leaving  the  salt  behind.  Weak  alcoholic 
liquors,  like  wine  and  cider,  may  be  concentrated  by  exposing  them 
to  cold  and  removing  the  layers  of  ice  as  they  form. 

564.  Change   of  volume.     At  the  moment  of  freezing, 
water   expands  with  great  force.     This   fact  is   familiar  to 
northern  housekeepers  in  the  breaking  of  utensils  in  which 
water  is  allowed  to  freeze.     Service  pipes  often  burst  unless 
a  little  stream  is  permitted  to  trickle  through  them.     Bomb 
shells  an  inch  thick,  filled  with  water,  have  been  burst  by 
the  freezing  of  the  water.     Cast  iron,  bismuth,  antimony, 
tin,  zinc,  and  some  of  their  alloys,  also  expand  on  solidify- 
ing.    These  substances  give  sharp  casts,  because,  when  the 
metal  sets,  the  expansion  forces  it  into  the  minute  cavities 
of  the  mold.     Most  substances,   except   those  enumerated, 
contract  on  solidifying ;  hence,  coins  of  copper,  silver,  and 
gold  require  to  be  stamped. 

565.  Latent  heat.     After  a  solid  begins  to  melt,  the  temper- 
ature remains  constant   nntil  the  whole  is  melted.     This  fact 
may  be  verified  by  watching  a  thermometer  immersed  in  a 
tumbler  filled  with  melting  ice.     A  large  amount  of  heat 
must  enter  a  pound  of  ice  at  32°,  before  it  can  be  changed 
to  water  at  32°.     A  pound  of  water  at  212°  mixed  with  a 
pound  of  water  at  32°,  gives  two  pounds  at  the  mean  tem- 
pt rature  of  122°;    but  a  pound  of  water  at  212°  mixed 
with  a  pound  of  ice  at   32°,  gives   two  pounds  of  water 
having  the  temperature  of  only  51°. 

In  this  case,  the  water  has  lost  161°,  while  the  ice  has 
gained  only  19°,  so  that  142°  have  disappeared  in  changing 
the  ice  to  water.  The  heat  is  not  lost,  for  an  equal  amount 
will  be  given  out  if  a  pound  of  water  is  converted  into  ice, 
but  because  this  is  not  sensible  to  the  thermometer,  the 


318  NATURAL  PHILOSOPHY. 

heat  which  a  body  absorbs  or  emits,  in  changing  its  mole- 
cular condition,  is  termed  latent  heat. 

The  latent  heat  of  water  is  of  the  greatest  value  in  nature.  1.  It 
retards  the  melting  of  snow.  To  change  a  pound  of  snow  at  32°  into 
water  at  32°,  requires  as  much  heat  as  to  warm  one  hundred  and  forty- 
two  pounds  of  water  one  degree.  If  it  were  not  for  this  provision, 
the  inhahitants  of  northern  valleys  would  be  exposed  to  terrific  inun- 
dations at  every  approach  of  spring. 

2.  The  melting  of  ice  withdraws  the  heat  from  surrounding  objects. 
A  "thawing  day"  frequently  feels  very  chilly.     Near  lake  Erie  the 
spring  is  so  much   retarded  by  the  melting  of  the  winter's  ice,  that 
generally  the  buds  of  trees  do  not  swell  until  the  danger  of  late  frosts 
is  past. 

3.  The  freezing  of  water  mitigates  the  sudden  setting  in  of  frosts, 
as  the  very  act  of  freezing  liberates  sufficient  heat  to  moderate  the 
effect    of    the    depression    of    temperature    on    surrounding    objects. 
Hence,  it  is  a  common  remark  that  the  weather  moderates  on  a  fall 
of  snow. 

566.  Every   solid   in   melting  has   its  own   latent  heat, 
which  is  called  the  fieat  of  fusion,  or  the  latent  heat  of  liquid*. 
The  amount  may  be  determined  by  the  method  of  mixtures. 
The  second  column  in  the  following  table  shows  the  number 
of  pounds  of  water  that  would  be  raised  one  degree  by  the 
solidifying  of  one  pound  of  each  substance  named. 

Latent  Heat  of  Liquids. 

In  °  F.  Water  -  1. 

Water 142.65  1.000 

Zinc 50.03  .365 

Tin '^-^ 

Sulphur  10.*-"'  -118 

Lead 9.68  .<>«7 

Mercury  <VI1  •"•">r> 

567.  Freezing  mixtures.     In  dissolving  solids,  as  in  molt- 
ing, a  certain   quantity  of  heat  becomes  latent.     Thus,    if 
snow  and   common    salt    !><•  mixed    together,  the  salt    causes 
the  snow  to  melt,  and  the  water  dissolves  the  salt,  so  that  both 


EVAPORATION.  319 

become  liquid,  and,  by  consequence,  a  large  amount  of  heat 
is  absorbed  from  the  surrounding  objects. 

This  is  the  mixture  used  for  freezing  ice  creams.  Two  parts  of 
snow  and  one  part  of  salt  will  reduce  the  temperature  to  — 4°  F. 
Two  parts  of  snow  mixed  with  three  parts  of  crystallized  chloride  of 
calcium  will  produce  a  cold  sufficient  to  freeze  mercury,  and  if  these 
substances,  and  the  containing  vessel,  be  previously  cooled,  a  cold  of 
—  50°  may  be  produced.  A  very  convenient  freezing  mixture  con- 
sists of  five  parts  of  common  hydrochloric  acid  and  eight  parts  of 
crystallized  sulphate  of  soda,  previously  reduced  to  powder. 

568.  Vaporization.     If  a  solid  be  exposed  to  sufficient 
heat,  when  the  expansive  force  of  the  heat  exerted  between 
its  molecules  equals  their  cohesive  force,  the  body  melts.    As 
the  temperature  rises,  the  expansive  force  becomes  greater 
than  the  cohesive,  and  the  liquid  passes  into  the  aeriform 
state,  as  soon  as  the  excess  of  expansive  force  exceeds  the 
atmospheric   pressure.     This,    the   third   effect   of   heat,    is 
termed  vaporization.     If  vaporization  takes  place  slowly  and 
quietly,  it  is  termed  evaporation,  but  if  the  liquid  is  agitated 
by  the  formation  of  bubbles  of  vapor,  the  process  is  termed 
ebullition,  or  boiling.     Some  solids,   as  iodine,  arsenic,   and 
camphor,    vaporize    without    becoming    liquids.       This    is 
termed  sublimation. 

569.  The  laws  of  evaporation  may  be  studied  by  intro- 
ducing a  small  quantity  of  ether,   or  other  volatile  liquid, 
through  a  barometer  tube,  into  the  Torricellian  vacuum  at 
the  top.     As   soon  as  the  liquid  reaches  the  vacuum,  it  is 
instantly  converted  into  vapor,  and  depresses  the  mercury 
by    its   elastic   force;     showing,    1.   All  volatile  liquids   in    a 
nirinim  are  instantly  vaporized.     If  successive  small  portions 
of  the  same  liquid   are  used,  the  mercury  continues  to  be 
depressed  until   a  point  is  reached  where  the  ether  remains 
liquid.     The  space  above  is  then   said   to   be   .« it  united,  and 
the  elastic  force  of  the  vapor  has  reached   its   maximum 
tension. 

If,  now,   the  tube  be  heated,  more  ether  will   vaporize, 


320 


NATURAL   PHILOSOPHY. 


and  the  mercury  will  be  further  depressed ;  but  if  the  tube 
be  cooled,  a  portion  of  the  vapor  will  be  condensed  into 
liquid,  and  the  mercury  will  rise.  Therefore,  2.  In  every 
space  void  of  air  the  maximum  tension  of  vapor  correspond* 
with  the  temperature. 

If  the  tube  be  plunged  in  a  deep  bath  of  mercury,  as  in 
Fig.  140,  and  the  saturated  vapor  be  exposed  to  increased 
tension,  by  depressing  the  tube,  a  portion  of  the  vapor  will 
become  liquid,  and  on  raising  the  tube  a  fresh  portion  will 
vaporize  under  diminished  pressure.  Therefore,  3.  Tfie 
maximum  tension  of  saturated  vapors  is  independent  of  tfie  press- 
ure. Non-saturated  vapors  obey  Mariotte's  law. 

If  the  first  experiment  be  per- 
formed with  several  different  vol- 
atile liquids,  Fig.  266,  each  having 
the  temperature  of  68°  F.,  the 
mercury  will  be  depressed,  in 
inches,  as  follows :  ether,  17 ; 
bisulphide  of  carbon,  12  ;  alcohol, 
1.7;  water,  0.7.  Hence,  4.  At 
the  same  temperature,  the  saturated 
vapors  of  different  liquids  possess 
different  elastic  force. 

If  two  liquids  which  do  not 
dissolve  each  other,  as  water  and 
bisulphide  of  carbon,  are  placed 
in  the  same  tube,  the  tension  of 
the  mixed  vapors  will  equal  the 
sum  of  the  two  taken  separately 
This  explains  the  remarkable  fact 
that  the  same  amount  of  water 

will  evaporate  in  a  space  filled  with  air,  as  in  a  vacuum 
of  equal  volume. 

570.  Evaporation  of  water  is  ^roing  on  constantly  in 
nature,  and  is  OIK-  of  the  me:m.-  by  which  the  earth  is  ren- 
dered fit  for  the  maintenance  of  life.  The  principal  cir- 


DEW  POINT.  321 

cumstances   which    influence    the   amount  and   rapidity   of 
evaporation  are  as  follows: 

1.  It  varies  with  the  temperature,  because  heat  increases 
the  elastic  force  of  vapors. 

2.  It  varies  with  the  amount  of  the  same  liquid  in  the 
atmosphere.     When  the  air  is  saturated,  evaporation  ceases; 
it  is  therefore  greatest  in  air  free  from  vapor. 

3.  It  is  assisted  by  the  renewal   of  the  air;  because,  if 
the  air  is  not  renewed  it  becomes  saturated.     Hence,  evap- 
oration is  more  rapid  in  a  breeze  than  in  still  air. 

4.  It  varies  with  the  extent  of  surface  exposed;  because, 
evaporation  proceeds  only  from  the  surface. 

5.  It  varies  inversely  with  the  pressure  on  the  surface  of 
the  liquid,  because  of  the  resistance  offered  to  the  escape  of 
the    vapor.     It   is  very  rapid  in   vacuo  and  less  rapid  in 
space  containing  air. 

Evaporation  may  go  on  at  very  low  temperatures.  Mercury  begins 
to  evaporate  at  60°  F.  Iodine,  camphor,  and  some  other  solids 
vaporize  at  ordinary  temperatures.  Snow  and  ice  disappear  from  the 
surface  of  the  earth  when  there  has  been  no  thawing.  Clothes  are 
dried  on  a  winter's  day,  when  the  thermometer  shows  a  temperature 
below  freezing.  A  warm  sultry  day  is  less  favorable  to  evaporation 
than  a  cold  day  with  a  brisk  wind. 

571.  Air  is  said  to  be  saturated  with  moisture  when  it 
contains  as  much  aqueous  vapor  as  it  can  hold  up  at  a 
given  temperature.  Air,  at  32°  F.,  can  absorb  yj-g-  part  of 
its  weight  of  aqueous  vapor.  For  every  increase  of  20°, 
the  capacity  of  air  for  moisture  is  nearly  doubled ;  at  fifty- 
two  degrees,  air  can  absorb  yfg-,  and  at  seventy-two  degrees, 
^  of  its  own  weight.  If  air,  saturated  with  moisture,  is 
cooled,  a  portion  will  be  deposited  as  dew.  The  tempera- 
ture at  which  this  deposit  occurs  is  called  the  dew  point. 
The  more  fully  the  air  is  saturated  with  moisture,  the 
nearer  will  the  dew  point  be  to  the  temperature  of  the 
atmosphere. 

N.  P.  21. 


322  NATURAL   PHILOSOPHY. 

The  dew  point  may  be  determined  with  sufficient  accuracy 
for  ordinary  purposes,  by  placing  ice  in  a  metallic  vessel 
containing  water,  and  noting,  by  a  thermometer,  the  temper- 
ature of  the  water  when  the  dew  begins  to  form  on  the 
outside  of  the  vessel.  The  higher  the  dew  point,  the  more 
abundant  will  be  the  deposit.  The  "sweating"  of  pitchers 
is  indicative  of  rain,  because  it  shows  that  the  air  is  nearly 
saturated  with  moisture,  which  will  fall,  if  the  temperature 
of  the  air  is  lowered  below  the  dewr  point. 

572.  Ebullition.  Tlie  temperature  at  which  liquid*  boll  *x 
constant  for  the  same  substance,  under  like  conditions.  Several 
circumstances  influence  the  boiling  point. 

1.  The  nature  of  the  liquid.  The  following  table  gives 
the  boiling  point  of  several  liquids  under  the  pressure  of 
one  atmosphere. 

Table  of  Boiling  Points. 


Protoxide  of  nitrogen...  —  157°  F. 

Carbonic  acid —  108.4 

Sulphurous  acid  -\-    17.6 

Ether  ..  94.8 


Bromine  145°.4  F. 

Alcohol 173.1 

Water    212. 

Mercury 602. 


2.  The  adhesion  of  the  liquid  to  the  vessel  which  contains 
it.     Water  sometimes  boils  in   a  glass  vessel  at  214°,  and 
in  a  glass  vessel  coated  with  shellac  as  high  as  221°.     The 
ebullition  then  takes  place  in  bursts,  the  temperature  fall- 
ing at  each   gust  of   vapor   to   212°.      By   throwing  iron 
filings  into  the  water,  the  boiling  point,  in  either  of  these 
cases,  is  reduced  to  212°. 

3.  Satis  in  solution  generally  increase  the   boiling   point. 
Thus,  a  saturated  solution  of  common  salt  boils  at  227°  F.; 
of  nitrate  of  potassa,  at  240°  F. ;    of  chloride  of  calcium, 
at  355°  F.     Substances  mechanically  suspended,  like  bran, 
saw-dust,  do  not  influence  the  boiling  point.      The  vapor 
which  arises  from  solutions  is  not  permanently  hotter  than 
the  steam  from  pure  water. 


BOILING   POINT. 


323 


4.  Variations  of  pressure  increase  or  diminish  the  boiling 
point,  because  n  //</"/'/  hnili  ivhen  the  tension  of  its  vapor  is 
equal  to  the  pre**nr<'  it  supports.  If  a  vessel  containing  ether 
be  placed  under  the  receiver  of  an  air  pump,  and  the  re- 
ceiver be  exhausted,  the  ether  will  boil  at  the  ordinary 
temperature.  Water  which  has  cooled  considerably  below 
the  boiling  point  may  be  again  made  to  boil  by  placing  it 
in  an  exhausted  receiver. 

The  culinary  paradox  illustrates 
the  same  principle.  A  flask  con- 
taining boiling  water  is  tightly 
corked  while  the  steam  is  escap- 
ing rapidly,  and  then  quickly  in- 
verted. If,  now,  a  stream  of  cold 
water  be  poured  on  the  bottom  of 
the  flask  the  boiling  will  be  re- 
newed, but  will  speedily  be  ar- 
rested if  hot  water  be  poured  on. 
The  reason  of  this  is,  the  cold 
water  condenses  the  steam  above 
the  water,  by  which  a  partial 
vacuum  is  produced. 

A  simple  proof  that  the  tension 
of  steam  is  equal  to  the  pressure 
of  the  atmosphere  is  obtained  by 
repeating  the  last  experiment 

with  a  tin  canister  instead  of  the  flask.  On  corking  the  canister  and 
pouring  cold  water  upon  it,  the  sudden  condensation  of  the  steam 
produces  a  vacuum,  and  the  canister  is  crushed  in  by  the  pressure  of 
the  external  air. 

The  sirup  of  sugar  and  many  vegetable  extracts  are  concentrated 
by  boiling  them  in  closed  vessels,  called  vacuum  pans.  A  powerful 
air  pump  constantly  removes  the  vapor  from  the  pan,  and,  conse- 
quently, the  evaporation  proceeds  at  a  temperature  so  low  that  it 
secures  the  sirup  or  extract  from  injury  by  heat. 

573.  A  variation  of  an  inch  in  the  barometric  column 
makes  a  difference  of  about  2°  F.  in  the  boiling  point  of 
water ;  so  that  within  the  range  of  atmospheric  pressure  in 
temperate  climates,  the  boiling  point  may  vary  5°  F. 


FIG.  267. 


NATURAL  PHILOSO /'//>'. 


foiling  'Points  of  Water  at  different  'Pressures. 


Boiling  point,  Barometer, 

0  F.  inches. 

184  16.676 

190  18.992 

195  21.124 

200  23.454 

205  25.46S 

210  28.744 

211  29.331 

212  29.922 

213  30.516 

214  31.120 

215  31.730 


Boiling  point,  Pressure  in 

0  F.  atmospheres. 

212  1 

iM'J.r>  2 

273.3  3 
291.2         4 
306.  5 
318.2  6 
329.6  7 

339.5  8 

348.4  9 

356.6  10 
415.4  20 


574.  The  temperature  of  the  boiling  point  of  water  is 
much   reduced   on  ascending  mountains,  in  consequence  of 
the  diminished  atmospheric  pressure. 

Soiling  'Point  of  Water  at  different  Altitudes. 

Above  the  Mean  height         Temperature, 

sea-level.  of  barometer.  °  F. 

Donkia  (Himalaya) +17337  15.442  179.9 

Mont  Blanc 15650  16.896  185.8 

Quito 9541  20.750  194.2 

Mount  Washington 6290  22.905  200.4 

Madrid  1995  27.720  208. 

London  0  29.922  212. 

Dead  sea  (below) -1316  31.496  214.4 

The  observation  of  the  boiling  point  of  water  at  any  particular 
elevation,  gives  a  ready  means  of  determining  its  elevation  above  sea- 
level,  a  difference  of  about  596  feet  of  ascent,  producing  a  variation 
of  1°  F.  in  the  boiling  point. 

575.  Marcet's   globe  is  used   to  estimate  the  tension  of 
high  pressure   steam.     It  consists  of  a  small   boiler,   fur- 
nished with   three  apertures,  through   one  of  which  a  ther- 
mometer  stem   is    pasn-d,   air   tight;    through   a   second   is 
inserted   a   glass  manometer  tube,  whose  lower  end  opm> 
under   mercury  placed   in   the  boiler;   the  third  aperture  is 
furnished  with  a  stop-cock.      The  boiler  is  half  filled  with 


SPHEROIDAL  STATE. 


325 


water.     On  applying  heat  it  will  be   found  that  so  long  as 
the  stop- cock  is  open,  the  temperature  of  the  boiling  will 
remain   steadily  at  212°  F.     Steam,  there- 
fore,   at  this   temperature,    has    an    elastic 
force  equal  to  the  pressure  of  one  atmos- 
phere. 

On  closing  the  cock,  the  steam,  which 
continues  to  rise  from  the  water,  increases 
in  elastic  force,  as  is  shown  by  the  rise  of 
mercury  in  the  manometer.  When  the 
mercury  in  the  manometer  stands  at  thirty 
inches,  the  tension  of  the  steam  will  be  in- 
creased one  atmosphere.  At  the  same  time 
the  boiling  point  gradually  rises,  and  at 
the  pressure  of  two  atmospheres  equals 
249°. 5  F.  The  elastic  force  of  the  steam 
increases  more  rapidly  than  the  rise  of  the 
boiling  point,  as  is  shown  by  the  preceding 
table.  For  this  reason,  high  pressure  steam 
is  more  economical  as  a  motive  power  than 
low  pressure. 

Steam,  heated  apart  from  water,  follows  the  general  law  for  the 
expansion  of  gases.  Such  steam  is  called  dry,  or  superheated  steam, 
and  is  applied  to  the  carbonization  of  wood,  and  the  rendering  of 
lard  and  tallow. 

576.  The  spheroidal  state  is  caused  by  the  slow  evap- 
oration of  a  liquid  in  apparent  contact  with  a  very  hot 
plate.  Drops  of  water  scattered  on  a  polished  surface  of 
high  temperature  do  not  flatten,  but  assume  an  ellipsoidal 
shape,  and  roll  quietly  about  until  they  evaporate,  without 
boiling.  This  experiment  may  be  performed  in  a  smooth 
metallic  capsule,  heated  over  a  lamp.  Into  this  any  vola- 
tile liquid  may  be  dropped  from  a  pipette.  Several  phe- 
nomena are  noticeable. 

1.  The  temperature  of  the  plate  must  be  greater  than 
the  boiling  point  of  the  liquid.  Thus,  the  plate  requires  to 


FIG.  268. 


326 


NATURAL    PHILOSOPHY. 


be   heated  to   340°  F.  to  produce  the  spheroidal  state  with 
water;  with  alcohol,  273°;  with  ether,  142°. 

2.  The   temperature   of  the   spheroid   is   lower  than  the 
boiling  points  of  the  liquids,  being,  for  water,  206°  F.;  for 
alcohol,  168°;  for  sulphurous  acid,  13°. 

3.  The  spheroid  does  not  touch   the  plate.     By  using  a 
plane  surface  of  silver,    the  light  of  a  taper  may  be  seen 
between  the  surface  and  the  liquid. 

If  the  source  of  heat  be  re- 
moved, the  temperature  of  the 
plate  will  fall  until  a  point  is 
reached  when  the  liquid  wets 
the  surface,  and  then  the  liquid 
will  boil  violently.  This  may 
be  shown  by  pouring  a  small 
quantity  of  water  into  a  copper 
flask,  intensely  heated,  and 
corking  the  flask  while  the 
liquid  is  in  the  spheroidal 
condition.  For  a  time  all  is 
quiet,  but  when  the  flask  lias 
cooled  sufficiently,  the  water 
will  be  suddenly  converted  into 
KI.J.  am.  steam,  and  the  cork  ejected 

with    violence.     It  is  probable 
that  boiler  explosions  are  sometimes  caused  in  a  similar  manner. 

577.  The  explanation  of  these  facts  is  that  as  soon  as 
the  drop  reaches  the  hot  surface  a  portion  of  it  is  converted 
into  vapor,  which  both  supports  the  spheroid  and  prevents 
the  conduction  of  heat  from  the  plate  to  the  liquid. 

The  temperature  of  sulphurous  acid,  in  the  spheroidal  state,  is 
13°  F. ;  hence,  it  is  capable  of  I'reexin^  water,  although  the  capsule 
containing  the  acid  may  be  ivbite  hot.  By  using  a  mixture  of  ether 
and  solid  carbonic  acid,  even  mercury  may  be  I'm/en.  So,  ton,  a 
moi-tened  band  may  be  drawn  without  injury  through  molten  iron  as 
it  runs  from  the  furnace.  The  moisture  of  the  band  is  converted 
into  a  non-conducting  envelope,  which  sullicieiit ly  protect-  the  skin 
during  the  short  period  of  its  immersion.  The  most  common  illus- 


LIQUEFACTION    OF    VAPORS. 


327 


(ration   of  the   spheroidal   state,  is  that  of  a  drop  of  water  rolling 
about  on  a  heated  stove. 

578.  The  liquefaction  of  vapors  may  be  produced  (1.) 
by  cooling,  (2.)  by  compression,  and  (3.)  by  chemical 
action. 

1.  A  saturated  vapor  condenses  at  its  boiling  point. 
The  process  of  distillation  illustrates  this  principle.  Dis- 
tillation is  used  (1.)  to  separate  liquids  from  solids,  as 
when  water  is  distilled  to  free  it  from  its  impurities ;  or 
(2.)  to  separate  a  volatile  fluid  from  another  less  volatile, 
as  when  alcohol  is  distilled  from  fermented  liquors.  The 
mixed  liquid  is  first  heated  in  a  retort  or  boiler,  the  vapors 
discharged  are  then  condensed  by  passing  them  through  a 


FIG.  270. 

pipe  kept  cool  by  being  surrounded  with  water.  Fig.  270 
represents  the  common  still.  The  boiler,  «,  contains  the 
liquid  to  be  evaporated  ;  the  spiral  tube,  called  the  worm, 
which  is  immersed  in  a  tank  of  cold  water,  receives  the 
vapors  to  be  condensed. 


328 


NATURAL    PHILOSOPHY. 


2.  If  a  closed  cylinder  be  filled  with  the  vapor  of  ether, 
and  this  compressed  by  a  piston,  as  soon  as  the  pressure  on 
the  piston  equals  the  maximum  tension  of  the  vapor,  the 
vapor  becomes  saturated,  and  if  the  pressure  be  continued, 
the  vapor  will  be  condensed  to  the  liquid  state. 

Faraday  succeeded  in 
liquefying  gases  by  the 
tension  of  their  own 

*SK,  vapor.     His  method  con- 

\  sists    in    inclosing    in   a 

^J— ^K  bent  glass  tube  the  sub- 

stances by  whose  chemi- 
cal action  the  gas  is  pro- 
duced, and  then  sealing 
the  shorter  leg.  In  pro- 
portion as  the  gas  is  lib- 
erated, the  pressure  in- 
creases and  ultimately 
it  liquefies  and  collects 
in  the  empty  end.  The 

condensation  is  further  assisted  by  immersing  the  shorter 
leg  in  a  freezing  mixture.     Fig.  271. 

In  this  way  cyanogen  is  readily  liquefied  by  heating  cyanide  of 
mercury  in  the  longer  end.  Larger  quantities  of  gases  are  condensed 
by  driving  the  vapors  by  means  of  force  pumps  into  strong  receivers. 
Under  the  joint  influence  of  cold  and  pressure,  nearly  all  the  gases 
have  been  liquefied. 

3.  Sulphuric  acid,  chloride  of  calcium,  and  several  other 
substances,  have  so  strong  an  affinity  for  the  vapor  of  water, 
that  they  will  absorb  it  from  the  air  even   when  it  is   not 
saturated.      Such    bodies,    placed   in    a   closed    space,    will 
quickly  abstract  all  the  moisture  from  it. 

579.  Latent  heat  of  vapors.  Since  the  temperature  of 
a  liquid  is  constant  during  ebullition,  it  follows  that  a  con- 
siderable quantity  of  li<-at  is  rendered  latent  in  producing 
the  molecular  chan.ir«-  from  liquid  to  vapor. 


FIG.  271. 


LATENT  HEAT   OF    VAPORS. 


329 


With  the  same  source  of  heat,  it  takes  about  5£  times  as  long  to 
change  boiling  water  into  vapor  as  to  raise  the  same  quantity  180 
degrees,  or  from  32°  to  212°;  hence,  the  latent  heat  of  steam  is 
180  X  6J,  or  about  960°.  The  latent  heat  of  vapors  is  more  accu- 
rately determined  by  distilling  them,  and  noting  the  rise  of  temper- 
ature caused  in  the  water  surrounding  the  worm  by  a  known  weight 
of  vapor.  The  application  of  both  these  methods  for  determining 
the  latent  heat  of  water  may  be  readily  made. 


FIG.  2:2. 

Arrange  a  glass  flask  and  beaker,  as  in  Fig.  272.  Pour  one  ounce 
of  water,  at  32°  F.,  into  the  flask,  and  5J  ounces  at  the  same  temper- 
ature into  the  beaker,  and  apply  heat.  Now  note  (1.)  the  time  re- 
quired to  raise  the  water  in  the  flask  to  boiling,  and  that  required  to 
change  the  boiling  water  to  steam.  The  latter  will  be  5£  times  longer 
than  the  former.  (2.)  When  the  water  in  the  flask  has  been  expelled, 
that  in  the  beaker  will  be  raised  to  the  boiling  point,  showing  that  an 
ounce  of  steam  is  competent  to  raise  5£  ounces  of  water  from  32°  to 
212°. 

Z,atent  Heat  of  Vapors. 


Water 966.6 

Alcohol 374.9 

Acetic  Acid..  .  183.4 


Ether ,. 162.8 

Bisulphide  of  Carbon 156. 

Bromine 82. 


580.  Cold  produced  by  evaporation.  Whatever  be  the 
heat  at  which  a  liquid  evaporates,  it  grows  sensibly  colder  in 
proportion  to  the  rapidity  of  evaporation,  unless  it  receives 
as  much  heat  from  external  bodies  as  is  rendered  latent. 


330 


NATURAL 


A  shower  of  rain  cools  the  air  by  absorbing  the  heat  during  evapor- 
ation. For  the  same  reason,  the  air  of  a  heated  room  cools  when  water 
is  sprinkled  on  the  floor.  Any  nieehanieal  eause  that  increases  the 
evaporation  enhances  the  effect.  A  breeze  or  current  of  air  produced 
by  fanning  causes  a  more  rapid  evaporation  of  the  perspiration,  and 
thereby  produces  a  refreshing  cooln* 

In  tropical  climates  water  is  cooled  by  the  use  of  porous  jars  placed 
in  a  draft  of  air.  A  small  quantity  percolates  through  the  pores,  and, 
on  evaporating,  abstracts  so  much  heat  from  the  remaining  liquid  as 
to  lower  its  temperature  considerably  below  that  of  the  surrounding 
air.  Ether  and  other  volatile  liquids  thrown  in  spray  on  portions 
of  the  body  may  so  benumb  them  by  cold  as  to  render  them  insensible 
to  pain  during  surgical  operations. 

581.  Water  may  be   frozen  by  its  own  evaporation,   by 
placing  a  thin  shallow  capsule,  filled  with  water,  over  strong 
sulphuric   acid,  under  the    receiver  of  an  air  pump.     On 
exhausting    the    receiver,    the    sulphuric   acid    absorbs   the 
vapors  as  fast  as  they  are  formed,  and  thus  a  very  rapid 
evaporation  of  the  water  ensues,  which  effects  the  freezing 
of  the  water. 

A  similar  result  is  produced  by 
means  of  the  cryophorus.  This  con- 
sists of  two  glass  bulbs,  connected  by 
a  long  tube.  In  making  the  instru- 
ment, one  of  the  bulbs  is  partially 
filled  with  water,  which  is  then 
made  to  boil  briskly  until  the  air 
is  expelled  by  the  steam,  and  the 
instrument  is  then  hermetically 
sealed.  On  cooling,  the  spare 
above  the  water  is  filled  only  with 
its  vapor.  If,  now,  the  empty  bulb, 
A.  is  plunged  into  a  free/ing  mix- 
ture, this  vapor  is  condensed  as  last 
as  it  is  formed,  and  evaporation 
occurs  so  rapidly  from  the  water  in 
the  other  bulb,  that  it  soon  begins 
to  freeze.  Fig.  273. 

582.  If  liquid   carbonic   acid   l»c   cx|n.>rd    io   tin-  air,  if 
evaporat<-  with  siirh  rapidity  that  a  portion  almost,  instantly 


VOLUMES   OF    VAPORS.  331 

solidifies,  and  produces  a  cold  of  106°  below  zero.  Mer- 
cury is  easily  frozen  by  pouring  upon  it  this  solid  carbonic 
acid  moistened  with  ether.  Natterer  obtained  a  cold  of 
—  220°  F.  by  evaporating  a  mixture  of  bisulphide  of  carbon 
and  liquid  protoxide  of  nitrogen  in  vacuo. 

583.  When  vapors   are   condensed  they  give  out  their 
latent   heat.     Water   may  be   boiled    in  wooden    tanks   by 
forcing  steam    into   it.      Buildings  are  frequently  warmed 
by  the  heat  of  steam  generated  in  a   boiler  placed  in  the 
basement.     To  this  end  it  is  conveyed  to  the  several  apart- 
ments by  coils  of  iron  pipe.     The  whole  amount  of  heat  in 
the  steam  is  the  sensible,  plus  the  latent  heat :  thus,  at  the 
boiling  point  a   pound   of  steam   contains   212  +  966.6  = 
1178.6  tfiennal  units. 

584.  Equal  volumes  of  different  liquids  produce  unequal 
volumes  of  vapor.     The  following  table  shows  the  volume 
of  vapor  furnished  by  one  cubic  inch  of  each  of  four  liquids, 
at  their  respective  boiling  points. 

Cubic  inches.  Boiling  point. 

Water  1696  212°  F. 

Alcohol 528  173 

Ether  298  95 

Oil  of  turpentine 193  314 

Water  furnishes,  bulk  for  bulk,  a  greater  amount  of  vapor  than 
any  other  liquid,  one  cubic  inch  expanding  to  nearly  a  cubic  foot. 
The  mechanical  value  of  the  expansive  force  of  different  vapors 
depends  upon  the  bulk  of  vapor  produced  from  an  equal  bulk  of 
each  liquid.  The  cost  of  fuel  in  generating  vapor  would  be  in  pro- 
portion to  the  latent  heat  for  equal  volumes,  but  experiments  show 
that,  for  equal  volumes,  the  latent  heat  of  these  liquids  is  not  far 
different.  There  would  be,  therefore,  no  economy  in  using  other 
liquids  in  place  of  water  in  the  steam  engine,  even  if  they  cost  no 
more  than  water. 

585.  The  incandescence  of  bodies  has  already  been  con- 
sidered in  (442a). 


332  NATURAL  PHILOSOPHY. 

586.  Recapitulation. 

The  effects  of  heat  are 

1.  The  expansion  and  contraction  of  bodies. 

2.  The  melting  and  solidifying  of  solids. 

3.  The  vaporization  and  condensation  of  liquids. 

4.  The  incandescence  and  cooling  of  solids. 

The  measurement  of  heat  may  regard 

1.  The  relative  intensity Temperature. 

2.  The  relative  quantity Specific  heat. 

3.  The  amount  absorbed  or  evolved  during  mole- 

cular changes Latent  heat. 

THE    DISTRIBUTION    OF   HEAT. 

587.  Any  heated  body  returns,   sooner  or  later,   to  the 
temperature  of  surrounding  bodies.     This  tendency  of  heat 
to  maintain  an   equilibrium   of  temperature,   is   due   to   a 
continued  exchange  of  molecular  motions  by  virtue  of  which 
every  molecule  tends  to  produce  in  contiguous  molecules  its 
own  rate  of  vibration.     Heat  may  be  transferred  from  one 
body  to  another  in  three  ways: 

1.  By  conduction,  or  from  molecule  to  molecule. 

2.  By  convection,  or  by  motion  among  molecules. 

3.  By  radiation,  or  by  thermal  undulations  through  space. 

588.  The  conducting   power  of  a  body  increases,    as  a 
general  rule,  with  its  density.     Hence  the  metals  are  good 
conductors ;    porous   solids,    poor   conductors ;    and    liquids 
ami  gases,  almost  non-conductors. 

The  conductibility  of  «o/*Vx  may  be  shown  by  equal  sized 
rods,  along  which  a  number  of  small  marbles  arc  fastened, 
at  equal  distances,  with  wax.  Fig.  274.  If  one  end  of 
this  rod  be  held  in  a  hot  flame,  the  heat  will  !><•  propagated 
from  molecule  to  molecule  along  the  rod,  and  its  gradual 
progress  will  bi!  manifested  by  the  successive  dropping  of 
the  marbles,  as  the  different  sections  of  the  rod  attain  the 
temperature  of  the  fusing  point  of  the  wax. 


CONDUCTION   OF  HEAT. 


333 


FlG.  274. 


That  different  solids  vary  much 
in  their  power  to  conduct  heat, 
may  be  shown  by  repeating  this 
experiment  with  rods  of  copper, 
iron,  brass,  glass,  etc. 

By  placing  thermo-multipliers 
at  equal  distances  on  similar 
metallic  rods,  the  following  table 
has  been  obtained. 


Relative  Thermal  Conductivity. 


Silver 100. 

Copper 73.6 

Gold 53.2 

Brass 23.$ 


Iron 11.9 

Lead 8.5 

Platinum 8.4 

Bismuth 1.8 


589.  That  liquids  are  poor  con- 
ductors may  be  shown  by  passing 
the  tube  of  an  air  thermometer 
through  a  funnel,  so  that  the  bulb 
shall  be  just  below  the  surface  when 
the  funnel  is  nearly  filled  with  water. 
Fig.  275.  Now,  if  ether  be  poured 
on  the  water  and  ignited,  the  ther- 
mometer will  be  but  slightly  af- 
fected. 

Gases,  when  confined,  are  almost 
non-conductors  of  heat.  Fibrous 
bodies,  like  wool  and  furs,  owe 
their  non-conducting  properties 
largely  to  the  air  which  is  confined 
between  their  meshes. 


FlG.  275. 


590.  The  conducting  power  of  a 
body  may  be  roughly  estimated  by  the  touch.  Thus,  sup- 
pose different  substances  to  be  compared  at  a  common  tem- 
perature (1.)  much  hotter,  and  afterward  (2.)  much  colder 
than  the  hand.  An  iron  rod,  if  heated  above  120°  F.,  will 


334  NATURAL   PHILOSOPHY. 

burn  the  hand,  because  it  conveys  its  heat  rapidly  to  the 
skin,  and  if  cooled  below  0°  F.,  will  blister  the  lips,  be- 
cause it  conveys  their  heat  away  so  rapidly. 

On  the  contrary,  a  bad  conductor  may  be  handled  with 
impunity,  within  even  greater  limits  of  temperature.  For 
the  same  reasons  an  oil  cloth  will  feel  warmer  or  colder 
than  a  carpet  in  the  same  room,  according  as  their  common 
temperature  is  greater  or  less  than  that  of  the  skin.  So, 
also,  the  oven  girls  of  Germany,  clad  in  woolen  garments, 
enter  ovens  heated  to  300°  F.  without  inconvenience, 
although  the  touch  of  any  metal  while  there  would  surely 
burn  them. 

Common  observation  furnishes  abundant  illustrations  of 
these  facts.  Water  is  sooner  heated  in  a  tin  cup  than  in 
one  of  porcelain,  because  the  metal  is  a  better  conductor  of 
heat.  Silver  conducts  away  heat  so  rapidly,  that  if  a  silver 
spoon  be  smoothly  wrapped  with  muslin,  water  may  be 
boiled  in  it  without  injuring  the  muslin.  Porous  bodies, 
like  ashes  and  plaster  of  Paris,  are  such  poor  conductors 
that,  if  the  hand  be  protected  with  a  thin  layer  of  either, 
it  may  carry  live  coals  without  danger.  So,  also,  woolen 
cloths,  wrapped  about  heated  irons,  protect  the  hands  of  the 
laundress. 

591.  The  practical  applications  of  these  principles  are 
very  numerous.  Thus,  non-conductors  are  used  (1.)  to 
prevent  the  escape  of  heat,  or  (2.)  to  exclude  heat. 

1.  Close  wooden  boxes,  Fig.  276,  lined  with  felt,  are  used  in  Nor- 
way to  economize  fuel  in  cooking.     For  instance,  a  kettle  containing 
water  and  vegetables  is  lir.-t  heated  on  the  stove  to  the  boiling  point, 
then  placed  within  the  felt  box  and  tightly  covered.     By  this  means 
suilirirnt  heat  i-  retained  to  cook  the  vegetables.     Double  doors  and 
windows,  which  inclose  a   layer  of  air,  prevent  the  escape  of  heat 
from  our  apartments.     For  the  same  reasons  furnaces  are  lined  with 
fire  brick.     So,  also,  straw  is  wrapped  about  tender  plants  to  prevent 
the  escape  of  their  heat.      In  a  -imilar  manner  a   layer  of  snow  pre- 
serves the  warmth  of  the  earth  during  the  chilling  blasts  of  winter. 

2.  Fire-proof  safes  are  made  with  double  walls  inclosing  non-con- 


USES    OF  NON-CONDUCTORS. 


335 


ducting  substaiuvs,  as  plaster  of  Paris  or  alum.  Ice  may  be  kept 
t'rom  melting  by  wrapping  about  it  a  thick  blanket.  Ice  houses  have 
double  walls,  inclosing  a  thick  layer  of  straw,  sawdust,  or  charcoal. 


FIG.  276. 

Water  coolers  are  constructed  in  the  same  manner.  The  table  mats 
placed  under  hot  dishes  protect  the  table.  Furnace  men  and  firemen 
wear  thick  woolen  garments  to  exclude  the  external  heat,  because 
this  is  greater  than  that  of  their  bodies. 

592.  The  main  object  of  clothing  is  to  prevent  the 
escape  of  heat  from  our  bodies.  The  conducting  power  of 
the  materials  used  for  clothing  is  in  this  order:  linen, 
cotton,  silk,  wool,  furs.  Hence,  with  equal  texture,  a 
woolen  garment  is  warmer  than  one  of  silk,  cotton,  or 
linen.  A  bed  quilt  containing  a  layer  of  paper  is  warm, 
because  the  paper  prevents  the  heat  from  escaping. 

The  furs  of  animals  in  cold  countries  are  finer  and  closer  than 
those  in  warm  countries.  The  feathers  and  down  of  northern  birds 
form  an  almost  perfect  non-conductor. 


336 


NATURAL    PHILOSOPHY. 


593.  Convection.     If  heat  be  applied  to  the  bottom  of  a 
flask  of  water,   containing  a  few  fragments  of  cochineal  or 
sawdust,   the   particles  of  the  liquid  will  be  seen  to  rise  as 

they  become  heated  and  expanded, 
while  other  colder  particles  descend 
from  the  side  to  supply  their 
place.  These  currents  will  then 
continue  until  the  whole  is  heated. 
This  process  of  circulation  among 
molecules  is  termed  convection. 
It  may  be  applied  to  the  heating 
of  liquids  and  gases,  but  not  of 
solids. 

In  heating  by  convection,  the  fire 
must  be  applied  beneath.  Thus,  on 
filling  a  test  tube  with  water,  and, 
holding  it  by  the  lower  part  so  that 
the  top  is  inclined  across  a  hot  flame, 
the  layers  of  water  at  the  top  may  be 
made  to  boil  without  communicating 
any  heat  to  the  hand,  owing  to  the 
low  conductibility  of  the  water. 

In  the  process  of  cooling  fluids,  the  currents  are  established  in  a 
contrary  direction.  The  upper  particles  become  specifically  heavier 
and  descend,  thereby  forcing  the  lighter  particles  upward  to  fill  their 
place.  Any  thing  that  hinders  this  free  circulation  retards  both  the 
heating  and  cooling  of  the  fluid.  Thus,  viscous  liquids,  like  molasses 
or  tar,  heat  and  cool  very  slowly. 

594.  The  convection  of  gases  is  more  energetic  than  that 
of  liquids,  because  their  expansion  by  heat  is  greater.     If 
"touch  paper,"  containing  chlorate  of  potassa,  be  burned  in 
the  vicinity  of  a  heated  body,  the  currents   of  air  arising 
from  it  may  be  traced  in  the  smoke.     The  air  which  thus 
rises  is  heated  by  convection. 

The  column  of  :iir  in  :i  chimney  becomes  heated  by  the  fire,  and 
i-  therein-  rendered  -jieeilieally  lighter  than  any  external  column  of 
air  and  rises.  I  fence,  the  external  air  will  enter  the  grate  with  a 
draft,  proportioned  both  to  the  height  of  the  chimney  and  the  in- 
tensity of  the  fire. 


Fio.  277. 


WINDS.  337 

595.  In  all  cases  of  convection  there  must  be  two  cur- 
rents in  opposite  directions. 

Thus,  if  a  lighted  candle  be  held  in  the  crack  of  a  door  which  opens 
between  two  apartments  of  different  temperatures,  a  current  of  warm,  air 
will  drive  the  flame  outward  from  the  heated  room,  at  the  top  of  the 
door,  while  the  current  of  cold  air  will  drive  the  flame  inward  at  the 
bottom  of  the  door. 

596.  Winds.     These  two  currents  are  always  attendant 
on  winds,   although  only  the   lower  one    admits  of  being 
accurately  traced.     The  atmosphere  is   heated   mainly  by 
convection.     The  surface   of  the   earth  is  warmed  by  the 
sun,  which  produces  little  direct  action   on  the  air.     The 
layers  of  air  in   contact  with   the  soil   become  heated  and 
rise,   while   colder  layers   descend   to   supply   their   place; 
thus  producing  upward  and  downward  currents.     Moreover, 
since  the  earth  is  not  heated  equally  in  all  places,  a  surface 
current  of  air  will  rush  from  colder  toward  warmer  local- 
ities, while  an  upper  current  will  proceed  at  the  same  time 
in  a  contrary  direction,  as  in  the  case  of  the  two  rooms 
above  mentioned. 

For  this  reason  a  surface  wind  might  always  be  expected  to  flow  from 
each  pole  toward  the  equator,  and  an  upper  current  to  flow  from  the 
equator  toward  the  poles.  The  direction  of  these  winds  is  modified 
by  the  daily  rotation  of  the  earth  on  its  axis  from  west  to  east.  In 
consequence  of  this  rotation,  fixed  objects  on  the  surface  have  a 
velocity  of  nine  hundred  and  eighty  miles  per  hour  at  the  equator 
and  a  successively  diminishing  rate  at  higher  latitudes,  until  at  the 
poles  the  motion  entirely  ceases. 

The  lower  current,  coming  from  the  poles,  partakes  of  the  motion 
of  the  surface,  and  is,  therefore,  moving  more  slowly  than  those 
regions  toward  which  it  proceeds.  Consequently  the  wind  appears  to 
come  from  a  direction  opposite  to  that  in  which  the  earth  is  moving, 
or  from  the  east,  with  a  velocity  equal  to  the  difference  in  the  two 
rates  of  motion. 

Hence,  it  results  that  two  constant  surface  currents  are  produced 

within  the  tropics  on  each  side  of  the  equator.     Their  direction  will 

be  the  resultant  of  the  effects  due  to  the  heat  and  the  diurnal  rotation. 

Therefore,  north  of  the  equator  there  will  be  a  steady  north-east  wind, 

N.  P.  22. 


338  NATURAL  PHILOSOPHY. 

and  south  of  the  equator  a  south-east  wind.     These  winds  are  called 
trade  winds  from  their  importance  to  navigation. 

The  upper  trade  winds  proceed  in  the  opposite  directions,  and  are 
sometimes  made  manifest  by  clouds  and  volcanoes.  As  these  winds 
go  northward  they  become  cooler,  and  gradually  descend  to  the  earth. 
The  variable  winds  in  our  latitude  are  frequently  caused  by  the  meeting 
and  crossing  of  the  upper  and  lower  currents. 

597.  Radiation.     It  is  evident  that  the  heat  of  the  sun 
does  not  reach   the  earth  by  conduction  or  by  convection, 
since  heat  is  propagated   by  either  of  these   methods  with 
exceeding   slowness.     A  heated  body  must,  therefore,  emit 
thermal   rays  which   have  the  power  of  exciting  vibrations 
in  aether  and  other  media,  in   the  same  manner  as  light. 
This  emission  of  heat   is  termed  radiation.     The   laws  of 
radiant  heat  are  identical  with  those  of  light,  and  the  phe- 
nomena are  in  all  respects  similar. 

598.  The  laws  of  radiant  heat.     If  a  heated  body  be 
suspended   in   space,  a  thermometer  placed  in  any  position 
around   it,  will   indicate  a  rise   in   temperature;    but  if  a 
screen  be  interposed,  the  thermometer  will  not  be  affected: 
hence, 

1.  Heat  radiates  in  straight  lines  in  all  directions. 
Since  heat  is  a  radiant  force, 

2.  The  intensity  of  radiant  heat  is  inversely  as  the  square  of 
the  distance  from  its  source. 

3.  The  intensity  of  radiant  Jieat  w  proportional  to  ifie  temper- 
ature of  its  source. 

599.  Theory  of  exchanges.     Since  no  body  is  known    to 
exist    at  the    temperature  of  absolute  zero,  all    bodies  must 
omit  thermal   waves  of  some  degree  of  intensity ;   while,  at 
the  same,  time,  they  receive  other  waves   from   surrounding 
bodies.     These  waves,  like  those  of  liLrlit,  may  and  do  cross 
o-ieh  other  without    disturbance.      If  the   sum  of  the  motion 
received  is  less  than  that  emitted,  the  body  becomes  cooler, 


REFLECTION   OF  HEAT.  339 

hut  if  greater,  the  body  becomes  warmer.  If  it  receives 
hack  just  as  much  heat  as  it  radiates,  it  remains  at  a  uni- 
form temperature. 

If  a  thermometer  be  placed  before  a  block  of  ice,  its  temperature  will 
fall,  because  the  ice  and  the  thermometer  are  both  sources  of  heat, 
and  the  thermometer  receives  less  heat  than  it  radiates.  The  ice 
does  not  radiate  cold,  for  the  opposite  result  would  have  been  attained 
if  the  bulb  of  the  thermometer  had  contained  frozen  mercury. 

600.  Bodies  differ  greatly  in  their  radiating  power;  but 
this  is  dependent  more  on  the  nature  of  their  surfaces  than 
of  their  substances. 

Thus,  if  a  canister  of  tin  have  one  of  its  sides  coated  with  lamp- 
black, another  with  paper,  a  third  scratched  or  tarnished,  and  the 
fourth  polished,  and  then  be  filled  with  boiling  water,  a  delicate 
thermometer  placed  at  each  side  in  succession  will  indicate  different 
temperatures. 

Lampblack  has  the  highest  emissive  power  known,  the  surfaces  of 
paper,  and  similar  loose  materials  are  next  in  order;  the  polished 
metals  are  the  poorest  radiators,  but  gain  in  radiating  power  in  pro- 
portion as  their  surfaces  are  tarnished.  Hence,  a  bright  silver  tea- 
pot filled  with  hot  water  will  retain  its  temperature  longer  than  one 
of  earthenware. 

Pipes  for  the  conveyance  of  steam,  should  be  kept  bright  until  they 
reach  the  rooms  where  the  heat  is  to  be  distributed,  and  there  their 
surfaces  should  be  blackened  to  increase  their  radiating  power. 

601.  Radiant  heat,  incident  on  any  surface,  may  be  (1.) 
reflected,  (2.)  refracted,  (3.)  absorbed,  or  (4.)  transmitted. 

602.  Reflection.     Substances  which  reflect  light  well,  are 
also  good  reflectors  of  heat.     The  proportion   of  incident 
heat  reflected  at  an   angle  of  forty-five  degrees,  from  cer- 
tain polished  surfaces,  is  shown  by  the  following: 

Table  of  'Reflecting  ^Powers. 


Silver 97 

Gold 95 

Brass 93 

Platinum .83 


Steel 82 

Zinc  81 

Iron  77 

Cast  iron 74 


340  NAT  URA  L    PHIL  OS  OPH  Y. 

Archimedes  is  said  to  have  burned  the  Koman  vessels  before  Syra- 
cuse by  concentrating  upon  them  the  solar  rays,  by  means  of  concave 
mirrors.  To  show  that  this  feat  is  possible,  Buffon  constructed  a 
concave  mirror  that  ignited  a  plank  of  tarred  wood  at  a  distance  of 
two  hundred  and  ten  feet. 

603.  Refraction.      When   a    solar  beam    is    transmitted 
through  a  prism  of  rock  salt,  and  the  spectrum  is  examined 
by  a  thermometer,  we  have  the  result  sketched  in  Fig.  222, 
showing, 

1.  That  the  thermal  rays  extend  through  and  beyond  the 
visible  spectrum,   and  are,  therefore,  of  different   refrangi- 
bility  and  wave  length. 

2.  That  the  maximum  heating  effect  lies  beyond  the  red, 
or  in  rays  of  low  refrangibility,  and,  consequently,  of  great 
wave  length,  but  invisible  to  the  eye. 

The  thermal  rays  which  accompany  light  are  called  lumi- 
nous  thermal  rays,  and  the  dark  rays  are  the  obscure  thermal 
rays. 

If  a  platinum  wire  is  heated,  it  first  emits  only  obscure  rays ;  as  it 
becomes  incandescent,  it  not  only  emits  luminous  rays,  but  also  adds 
to  the  intensity  of  the  obscure  vibrations.  Hence,  the  hotter  a  body 
the  more  numerous  are  the  rays,  and  the  more  intense  are  each  set 
of  vibrations.  The  obscure  and  the  luminous  thermal  rays  are  gov- 
erned by  the  same  laws,  but  differ  from  each  other  exactly  as  one  color 
differs  from  another. 

604.  Absorption    and    transmission.     Most    transparent 
bodies  transmit  the  rays  of  heat  from   the  sun  as  well  as 
those  of  light;   but  will  not  equally  transmit  the   thermal 
rays  from  artificial  sources.     Thus,  the  heat  of  the  sun  will 
readily  pass  through  glass  windows  and  warm  a  room,  while 
the  same  thickness  of  glass  would   effectually  shut  off  the 
heat  of  a  fire.     A  substance  that   transmits  heat  is  railed 
diatJiermanous,    and    one    that   is   opa<|ii»i    to    heat    is    called 
athermanous.        Incident  rays  not  transmitted  are  either  re- 
flected   or    absorbed.      Only    the    rays    absorbed    have    any 
effect  in  warm  ing  th<-  body. 


1>[ATHERMANCY.  341 

^  605.  The  diathermancy  of  a  body  varies  both  with  the 
nature  of  the  substance  and  the  quality  of  the  heat.  The 
following  table  shows  the  proportion  of  one  hundred  inci- 
dent rays,  coming  from  different  sources,  that  will  be  trans- 
mitted by  different  substances,  cut  in  plates  0.1  of  an  inch 
in  thickness: 

Naked       Incandescent        Copper        Copper 
flame.          platinum.        at  752°  F.    at  212°  F. 

Rock  salt 92.3  92.3  92.3  92.3 

Sulphur 74  77  60  54 

Iceland  spar 39  28  6  0 

Glass 39  24  6  0 

Clear  quartz 38  28  6  3 

Smoky  quartz 37  28  6  3 

Alum  9200 

Rock  candy  8100 

Ice 6  0.5  0  0 

606.  This  table  shows  that  diathermancy  and  trans- 
parency are  analogous,  but  not  identical  properties.  The 
different  sources  of  heat  correspond  to  different  colored 
flames,  and  the  plates  or  screens  to  different  colored 
glasses. 

Plate  glass  is  nearly  transparent  for  all  rays  of  light,  as  rock  salt 
is  diathermanous  for  all  rays  of  heat.  In  either  substance  the  vibra- 
tions not  transmitted  are  mostly  reflected.  Red  glass  transmits  only 
red  rays,  alum  transmits  only  luminous  thermal  rays ;  but  these  sub- 
stances absorb  most  of  the  other  rays. 

Luminous  or  thermal  rays  which  have  traversed  one  plate  will 
traverse  another  plate  of  the  same  material  with  but  little  loss  of 
intensity.  Each  substance  acts  as  a  sieve,  and  transmits  only  those 
rays  which  are  able  to  penetrate  the  material  of  the  screen.  Thus 
light  which  has  passed  through  one  plate  of  red  glass  will  be  largely 
transmitted  by  a  second  red  glass :  so,  also,  if  the  nine  thermal  rays 
transmitted  by  a  plate  of  alum  be  incident  on  a  second  plate  of  alum, 
ninety  per  cent.,  or  eight  of  the  rays  will  be  again  transmitted. 

In  general  any  medium  is  diathermanous  for  certain  rays,  and  ab- 
sorbs the  greater  portion  of  the  remainder.  Glass  is  diathermanous 
for  rays  of  high  refrangibility,  but  almost,  if  not  quite,  athermanous 
for  obscure  rays. 


342 


NA  T  URA  L   PHIL  OS  OP II Y. 


If  iodine  be  dissolved  in  bisulphide  of  earbon,  it  will  form  a  very  dark 
and  opaque  solution.  If  light  from  any  source  be  transmitted  through 
layers  of  this  iodine  solution,  about  one-tenth  of  an  inch  in  thick- 
ness, the  luminous  rays  will  be  entirely  absorbed,  but  the  obscure 
rays  will  pass  freely.  These  invisible  rays  may  be  concent  rated  by 
lenses  of  rock  salt,  and  made  to  melt  and  even  ignite  solid  bodies. 
The  same  effect  may  be  produced  by  concentrating  the  luminous  solar 
rays  with  lenses  of  glass,  or  even  of  ice. 

607.  The  following  table  of  diathermancy  of  fluids  was 
obtained  by  transmitting  the  heat  of  an  Argand  lamp 
through  layers  of  fluids  thirty-six  hundredth*  of  an  inch 
in  thickness,  contained  in  glass  cells.  It  must  be  borne  in 
mind  that  the  glass  employed  permitted  only  the  luminous 
rays  to  enter  the  liquid.  The  table  shows  the  per  centage 
of  the  incident  rays  transmitted. 


Bisulphide  of  carbon 63 

Turpentine 31 

Olive  oil...  »  30 


Alcohol  15 

Solutions  of  salt  and  sugar 12 

Pure  water 11 


608.  The  simple  gases,  hydrogen,  nitrogen,  oxygen,  and 
dry  air,  are  almost  perfectly  diathermanous,  but  some  of 
the  compound  gases  have  great  absorptive  power,  especially 
for  dark  heat.  This  is  strikingly  shown  by  the  following 
table  of  the  absorption  of  heat  by  various  gases,  each  at 
the  tension  of  one  inch,  barometric  pressure,  in  comparison 
with  dry  air. 


Air 

Oxygen 

Nitrogen 

Hydrogen   


Carbonic  oxide  ..................  7~>0 

Sulphide  of  hydrogen  .........  2100 

Ammonia  .........................  7200 

Oletiant   gtis  ........... 


Chlorine oO    Sulphurous  acid. 


8800 


I-Yoni  this  it  will  be  seen  that  minute  quantities  of  these  .u;a>e-  nui-t 
have  great  effect  on  the  diathermancy  of  tin-  atmo-phere.  It'  our 
atmo-pheiv  were  coal  gas,  only  twenty  per  cent,  of  the  thermal  rays 
from  tin- .-mi  could  reach  the  earth.  With  regard  to  vapors,  it  may  In- 
said  that  tln-ir  ab-orptive  power  is  in  the  same  order  as  the  liquids 
from  which  they  are  derived.  Hence,  by  reference  to  the  previous 
table,  it  will  be  seen  that  aqueous  vapor  is  a  powerful  absorbent. 


ABSORPTION   OF  HEAT.  343 

609.  The  absorptive  effect  of  the  aqueous  vapor  in  the 
atmosphere   is   calculated    to   be   more   than    one    hundred 
times  that  of  dry  air.     The  absorptive  power  of  aqueous 
vapor   for  obscure  rays,   is  many  times    greater  than    for 
luminous  rays.     The  solar  rays  pass  with  comparative  free- 
dom to  the  earth,  and  are  expended  in  warming  the  earth. 
The   heated  earth   radiates   only   obscure   rays,   which   are 
absorbed  by  the  atmosphere,  and,  consequently,  its  rate  of 
cooling  is  diminished.     In  central  Asia  the  nights  are  very 
cold  and   the  winters  almost   unendurable,  because  of  the 
dryness  of  the  air. 

610.  If  heat   falls   on   a  body   not  diathermanous,    the 
rays  that  are  not  reflected  are  absorbed.     Hence,  the  ab- 
sorbing power  of  athermanous  bodies  is  inversely  as  their 
reflecting  power.     That  is,  good  absorbents  are  bad  reflect- 
ors.    As  bodies   must  give   out   in   cooling  the  heat   they 
have  absorbed,  so  good  absorbents  are  good  radiators.     The 
relation   between  the    radiating,    reflecting,    and    absorbent 
powers  will  be  seen  by  the  following  table: 

Radiation.         Absorption.        Reflection. 

Lampblack 100  100  0 

Indian  ink 85  96  4 

White  lead 100  53  47 

Isinglass 91  52  48 

Gum  lac 72  43  57 

Polished  metal 12  14  86 

611.  The  formation  of  dew  may  be  explained  in  accord- 
ance with  these  principles.     As  soon  as  the  sun  sinks  below 
the  horizon,  the  heat  radiated  from  the  surface  is  no  longer 
compensated  by  the  solar  rays,  and,  consequently,  the  tem- 
perature of  the  surface  is  speedily  reduced  below7  that  of  the 
stratum  of  air  in  contact  with  it.    If  this  stratum  is  charged 
with  moisture,  the  dew  will  be  deposited  on  any  good  radi- 
ator, as  grass  or  leaves,  but  will  not  ordinarily  collect  on 
metallic  surfaces. 

Clouds  or  overhanging  branches  of  trees  prevent  the  de- 
position of  dew,  because   they  return   the  heat  to  objects 


344  NATURAL    PHILOSOPHY. 

beneath  them.  So,  also,  a  fresh  breeze,  which  brings  new 
layers  of  air  in  contact  with  the  surface,  prevents  the  reduc- 
tion of  the  temperature  and  the  formation  of  dew.  The 
dew  will,  therefore,  be  most  abundant  on  still,  cloudless 
nights.  If  the  temperature  sinks  below  32°  F.,  the  dew  is 
deposited  in  needles  of  ice,  which  constitute  white,  or  hoar 
frost. 

612.  All  the  phenomena  of  radiant  heat  show  a  remark- 
able analogy  to  those  of  light.     If,  now,  we  add  that  heat 
may  be  polarized  and  made  to  exhibit  the  phenomena  of 
diffraction   and  interference,  we  can  hardly  resist  the  con- 
clusion that  heat  and  light  are  identical. 

613.  Applications.    The  hot  beds  of  the  gardeners  act  by 
economizing  the  heat  of  the  sun.     The  solar  rays  pass  freely 
through   the  glass  and  are  absorbed  by  the  earth  and  the 
plants.    These  emit  only  obscure  rays,  which  can  not  escape 
through  the  glass.     The  air  confined  in  the  bed  may  thus 
attain  a  temperature  above  that  of  the  exterior  atmosphere. 
The  effect  is  enhanced  by  coating  the  wooden  sides  of  the 
bed  with  lampblack. 

Meat  roasters  are  constructed  of  polished  tin,  to  reflect 
all  the  rays  of  the  fire  upon  the  article  cooking. 

Franklin  found  by  placing  pieces  of  cloth  of  the  same 
texture  but  of  different  colors  upon  newly  fallen  snow,  that 
the  snow  melted  under  the  cloth  with  the  greater  rapidity  the 
darker  the  tint.  This  fact  shows  that  for  solar  rays  clothes 
of  dark  color  are  better  absorbents  and  poorer  reflectors  than 
white.  Hence,  as  the  object  of  clothing  is  to  preserve  the 
body  from  sudden  changes  in  temperature,  white  garments 
are  preferable  to  black. 

Other  experiments  show  that  this  difference  in  the  ab- 
sorptive effect  of  colors  entirely  fails  f«.r  heat  from  artificial 
sources.  It  so  happens  that  many  good  reflectors  arc  white, 
and  nmny  good  absorbents  and  radiators  arc  dark  ;  but  their 
respective  powers  are  due  rather  to  the  molecular  condition 
of  their  surfaces  than  to  their  colors. 


SOURCES    OF  HEAT. 
614.  Recapitulation. 


345 


Conduction. 


{^onaucuon. 
Convection. 
Radiation. 


Radiant  heat,  incident  on  a  body,  may  be. 


Reflected. 
Refracted. 
Absorbed. 
Transmitted. 


THE    SOURCES   OF   HEAT. 


615.  The   sources   of  heat  may   be   comprised   in   three 
classes:   (1.)  physical,  (2.)  chemical,  (3.)  mechanical. 

Physical  sources.  The  sun  is  the  ultimate  source  of 
most  of  the  available  heat  of  the  globe.  To  measure  the 
intensity  of  the  radiant  heat  of  the  sun  an  instrument, 
called  the  pyrheliometer,  has  been 
devised.  It  consists  of  a  thermom- 
eter, d,  whose  bulb  is  inclosed  in  a 
shallow  cylindrical  box  of  silver, 
A,  which  is  filled  with  water.  The 
upper  surface  of  the  box  is  coated 
with  lampblack.  At  the  other  ex- 
tremity of  the  instrument  is  a  disk 
of  the  same  diameter  as  the  box. 
The  face  of  the  box  will  be  perpen- 
dicular to  the  sun's  rays  when  the 
shadow  of  the  box  exactly  coincides 
with  the  disk. 

The  measurement  requires  three 
steps :  FI 

1.  The  instrument,  sheltered  from  the  sun,  is  turned  toward  the  clear 
sky  for  five  minutes.     It  will  lose,  by  its  own  radiation,  an  amount 
of  heat  which  we  may  denote  by  r. 

2.  The  blackened   face  is  turned  to  the  sun  for  five  minutes,  and 
will   absorb  a  certain    quantity  of  heat.     Denote  the   gain   in    heat 
by  A. 


346  NATURAL    PHILOSOPHY. 

::.  While  heated,  it  is  again  turned  to  the  clear  sky  for  five  minutes. 
and  will  lose  heat  equal  to  r'. 

Now,  since  r  denotes  the  loss  by  radiation  into  a  clear  sky  before 
heating,  and  r'  the  loss  after  heating,  the  radiation  during  the  heat- 
ing will  be  the  mean  between  the  two,  or  r-*-.  As  this  radiation  is 
going  on  even  while  the  blackened  face  is  absorbing  the  sun's  rays,  the 
whole  heating  effect  of  the  sun,  during  the  five  minutes  exposure  will 
e4ual  A  +  r-*£. 

Now,  as  the  area  of  the  face  is  known,  we  may  express  the  effect 
of  the  sun's  heat  on  any  given  surface  by  stating  that  it  is  competent 
to  raise  so  much  water  so  many  degrees  in  temperature,  or  to  melt  a 
film  of  ice  of  proportionate  thickness. 

616.  By  these  measurements  it  has  been  found  that  the 
r>  lilcal  rays  of  the  sun  are  competent  to  melt  a  film  of  ice 
.00728   of  an   inch   thick,  every  minute.     The  intensity  of 
the  rays  decreases  with  their  obliquity,  and  the  atmosphere 
absorbs  0.4  of  the  entire  radiation  of  the  sun  received  by  the 
eartb.     Taking  these  considerations  into  account,  it  is  calcu- 
lated that,   if  the  earth  had  no  atmosphere,  the  solar  beat 
received  by  the  earth  in  one  year  would  melt  a  layer  of  ice 
completely  enveloping  it  to  the  depth  of  one  hundred  feet. 

To  compute  the  total  radiation  of  the  sun,  imagine  a 
hollow  sphere  to  surround  it  at  the  distance  of  the  earth 
from  the  sun.  Two  thousand  one  hundred  and  twenty-nine 
millions  of  globes,  as  large  as  the  earth,  placed  one  against 
the  other,  would  be  required  to  cover  this  imaginary  sphere; 
hence,  the  total  heat  emitted  by  the  sun  is  two  thousand 
one  hundred  and  twenty-nine  million  times  that  which 
reaches  our  earth. 

617.  It  has  been  estimated  that  the  fixed  stars  annually 
radiate   sufficient  heat  to  the  earth  to  melt  an  envelope  of 
ice  eighty  feet  in    thickness.     It   is  evident   that  were   the 
supply  of  either  solar  or  stellar  heat  cut  off.  tin-  life  of  the 
globe  would  soon  be  destroyed. 


618.  The  phenomena  of  volcanoes  and  hot  springs  a 
the  existence  of  intensely  heated   fluid   matter  within   the 


CHEMICAL   SOURCES.  347 

earth  itself.  The  heat  received  from  celestial  bodies  does 
not  penetrate  the  earth's  surface  more  than  one  hundred 
feet.  If  thermometers  are  carried  to  greater  depths  in 
mines  and  in  artesian  wells,  the  temperature  is  found  to 
rise  quite  regularly  at  the  average  rate  of  1°  F.  for  every 
fifty-four  feet  of  descent. 

At  this  rate,  depths  would  soon  be  reached  at  which  all  known 
rocks  would  melt,  so  that  it  is  not  probable  that  the  thickness  of  the 
solid  crust  of  the  earth  much  exceeds  one  hundred  miles.  Neverthe- 
less, from  the  imperfect  conductibility  of  this  crust,  it  does  not 
appear  that  the  central  heat  of  the  globe  affects  the  annual  tempera- 
ture of  the  surface  more  than  one-twentieth  of  a  degree. 

Besides  these  physical  sources  of  heat,  may  be  mentioned  electricity 
and  the  heat  attending  molecular  changes,  as  absorption,  capillary 
action,  and  the  phenomena  of  liquefaction  and  solidification. 

619.  Chemical  sources.  When  any  two  bodies  unite  in 
chemical  combination  there  is  usually  an  evolution  of  heat. 
The  amount  of  heat  evolved  is  always  the  same ;  but  if  the 
combination  takes  place  slowly,  the  heat  can  not  be  measured 
for  any  single  moment. 

Combustion  is  the  rapid  combination  of  two  or  more  sub- 
stances, attended  by  the  evolution  of  heat  and  usually  of 
light.  Thus,  if  water  be  poured  upon  quicklime,  the  two 
will  combine,  and  may  evolve  heat  sufficient  to  boil  the 
water.  If  a  grain  of  iodine  be  placed  upon  a  slip  of  phos- 
phorus they  will  kindle  into  a  flame,  which  will  afterward 
be  continued  by  the  oxygen  of  the  air. 

Ordinary  combustion  is  due  to  the  union  of  the  oxygen  of 
the  air  with  the  carbon  and  hydrogen  contained  in  the  coals, 
oils,  fats,  and  gases  of  our  fires  and  flames.  The  rusting 
of  iron,  the  decay  of  wrood,  the  process  of  fermentation,  are 
examples  of  slow  combustion  with  oxygen. 

Animal  heat  is  due  to  slow  combustion.  In  respiration 
(1.)  oxygen  passes  through  the  cell-walls  of  the  lungs  by  os- 
mosis, and  is  absorbed  by  the  blood,  which  it  thereby  renders 
arterial,  (2.)  This  arterial  blood  is  then  distributed  to  the 


348  NATURAL   PHILOSOPHY. 

capillaries  of  the  different  organs,  where  a  greater  or  less 
consumption  of  carbon  takes  place,  with  the  evolution  of 
carbonic  acid.  (3.)  The  blood  charged  with  this  carbonic 
acid  is  rendered  venous  and  returned  to  the  lungs,  where 
the  carbonic  acid  is  exhaled  by  osmosis,  and  a  fresh  supply 
of  oxygen  absorbed. 

The  supply  of  carbon  is  furnished  by  the  tissues,  which 
are  themselves  maintained  by  the  processes  of  digestion  and 
nutrition.  Thus,  in  one  sense,  our  animal  heat  is  main- 
tained by  the  indirect  combustion  of  food  and  air. 

The  following  table  shows  the  total  heat  of  combustion 
with  oxygen  of  one  pound  of  each  of  the  substances  named, 
expressed  in  thermal  units  of  one  pound  of  water  raised 
one  degree  F. : 

Pounds  of 

oxygen  Thermal  Compound 

Symbol.  consumed.  units.  formed. 

Hydrogen H  8  62032  HO 

Carbon  C  \\  4344  CO 

Carbon  C  2*  14544  CO2 

Carbonic  oxide  CO                    i  4376  CO2 

Sulphur S  1  4032  SO2 

Phosphorus P  \\  10344  PO5 

Iron Fe  &  2836  Fe3O4 

Alcohol  C4II6O2  3£  12929 

Olefiantgas C4H*  3£  21344 

Marsh  gas C2H4  4  23513 

620.  It  is  to  be  noted  that  the  total  heat  is  the  same, 
whether  the    oxidation  be  reached  at  once  or  by  successive 
steps. 

For  example,  one  pound  of  carbon,  in  burning  imperfectly,  forms 
2J  pounds  of  carbonic  oxide,  and  evolves  4344  units  of  heat.  If 
thrse  2J  pounds  of  carbonic  oxide  be  burned  they  will  evolve  10210 
units  of  heat  in  forming  carbonic  acid,  making  4344  -f  10210  -  14554 
units  of  heat,  or  the  same  amount  tlint  would  be  obtained  by  the 
complete  combustion  of  one  pound  of  carbon. 

621.  The   mechanical   sources   of   heat   are   percussion, 

compression,  and  friction.  (1.)  If  a  nail  be  pounded  on  an 
anvil  with  light,  rapid  blows,  it  may  be  made  red  hot  by 


MECHANICAL    SOURCES. 


349 


percussion.     (2.)  The  production  of  heat  by  the  compression 
of  gases  may  be  shown  by  the  pneumatic  syringe,  Fig.  279. 

This  instrument  consists  of  a  thick  glass  tube,  in  which  a  piston 
works  air  tight.  To  use  it,  a  piece  of  tinder  is  placed  on  the  bottom 
of  the  piston,  which  is  then  driven  suddenly  downward  in  the  tube. 


Flo.  279. 

The  air  in  the  tube  is  thus  compressed,  and  liberates  so  much  heat 
as  to  set  fire  to  the  tinder,  which  is  seen  to  burn  when  the  piston  is 
withdrawn.  The  disengagement  of  heat  is  found  to  be  proportional 
to  the  reduction  in  volume,  and  the  consequent  increase  in  density. 

(3.)  The  friction  of  two  bodies  always  produces  heat, 
which  is  the  greater  the  more  rapid  the  motion  and  the 
greater  the  pressure.  It  is  the  heat  thus  produced  that 
ignites  the  phosphorus  on  the  end  of  a  match,  and  that 
causes  the  axles  of  car  wheels  to  ignite  the  wood  work  in 
their  immediate  vicinity.  Savages  procure  fire  by  revolving 
the  eod  of  one  piece  of  dry  wood  in  the  cavity  of  another. 


FIG.  280. 

An  experimental  demonstration  of  the  same  fact  may  be  strikingly 
shown  by  attaching  to  a  whirling-table  a  brass  tube  filled  with  water 
and  corked.  Fig.  280.  If,  when  the  tube  is  revolving  rapidly,  a 


350  NATURAL   PHILOSOPHY. 

clamp,  P,  of  two  pieces  of  oak  is  pressed  against  the  tube,  the  heat 
evolved  by  the  friction  of  the  wood  against  the  tube,  will  be  sufficient 
to  boil  the  water  in  a  very  few  minutes. 


THE  DYNAMICAL  THEORY  OF  HEAT. 

622.  The  dynamical  theory  of  heat,  which  assumes  that 
heat  is  a  mode  of  molecular  motion,  affords  a  satisfactory 
explanation  of  these  various  phenomena.     In  all   cases  of 
friction,  compression,  and  percussion,  a  certain  amount  of 
mechanical  force  is  arrested,  the  energy  of  its  visible  motion 
is  spent  in  producing  molecular  motion,  and  is  thus  trans- 
formed into  heat.     The  quantity  of  heat  evolved  is  in  proportion 
to  the  mechanical  force  expended. 

Thus,  when  air  is  compressed,  the  rise  in  temperature  is 
due  to  the  mechanical  effect  or  work  which  must  be  spent 
in  driving  the  particles  of  the  air  nearer  together. 

Conversely,  Heat  is  consumed  in  effecting  mechanical  work. 
Let  a  cylinder  filled  with  compressed  air  be  cooled  to  the 
temperature  of  surrounding  bodies.  Its  elastic  force  is 
competent  to  produce  mechanical  work,  (1.)  by  moving  a 
piston,  or  (2.)  in  displacing  the  air  in  front  of  the  cylinder. 
If,  now  this  air  is  allowed  to  expand  into  the  atmosphere, 
the  air  will  be  chilled,  because  mechanical  work  has  been 
performed  by  the  expenditure  of  the  heat  to  which  the 
elastic  force  of  the  air  was  due. 

623,  The  relation  which  exists  between  heat  and  work, 
is  known  as  the  mechanical  equivalent  of  heat,  or,  simply,  as 
Joule's  equivalent. 

To  determine  it  for  gases,  suppose  a  tall  cylindrical 
vessel,  C,  whose  section  is  equal  to  a  square  foot, 

and  let  I'  1'  he  a  piston  without  weight  moving  in 
the  cylinder.  If  the  piston  he  placed  so  that  tiie 
height,  A  P  is  one  loot,  it  will  inclose  a  cubic  foot 
of  air.  Now,  if  this  air  he  heated  -I'M)0  F.,  its 
volume  will  he  doubled,  and  will  raise  the  piston 
Fro.  281.  one  foot,  or  to  I"  1".  In  rising  it  has  overcome 


JOULE'S  EQUIVA LEN T. 


351 


the  pressure  of  the  atmosphere  above  the  piston,  or  has  lifted 
15  X  144  —  21GO  pounds  one  foot,  and  has  performed  work  equal 
to  iMiiO  foot-pounds. 

With  the  same  amount  of  heat,  only  about  one-fourth  as  much 
water  would  have  been  raised  490°,  because  the  specific  heat  of  air 
is  0.24  that  of  water.  The  weight  of  a  cubic  foot  of  air  is  .08  pounds, 
hence  the  heat  imparted  to  perform  the  work  of  the  air,  would  have 
heated  only  0.08  X  0.24  =  .0192  pounds  of  water  490°.  This  is  equiv- 
alent to  9.4  pounds  of  water  heated  1°  F.  Hence,  9.4  thermal  units 
have  been  required  to  raise  2160  pounds  one  foot  high,  by  the  expan- 
sion of  the  air. 

If  the  piston  had  been  fixed  so  as  to  retain  the  air  at  a 
roHxtnnt  volume  while  being  heated,  the  quantity  of  heat  re- 
quired to  raise  its  temperature  490°  would  have  been  less 
than  when  expanding  under  a  constant  pressure,  in  the  ratio 
of  1.421  :  1.  Hence,  the  thermal  units  required  to  raise 
the  temperature  of  the  cubic  foot  of  air  when  kept  at  a 
constant  volume  is  found  to  be  9.4  -f-  1.421  =6.6  units. 
Deducting  6.6  units  from  9.4  units,  we  find  that  the  excess 
of  heat  imparted  to  the  air  when  permitted  to  expand,  is 
competent  to  raise  2.8  pounds  of  water  1°  F.  This  excess 
has  been  employed  in  performing  the  work  of  lifting  2160 
pounds  one  foot  high.  Dividing  2160  by  2.8,  we  find  that 
the  quantity  of  heat  required  to  raise  one  pound  of  water 
1°  F.  is  competent  to  lift  772  pounds  a  foot  high.  This  is, 
therefore,  the  mechan- 
ical equivalent  of  one 
thermal  unit. 

624.  Joule  deter- 
mined the  mechanical 
equivalent  of  heat  by 
the  friction  of  fluids. 
A  metallic  box.  Fig. 
282,  was  provided 
with  eight  sets  of 
paddles,  which  were 
made  to  revolve  be- 


•352  NATURAL  PHILOSOPHY. 

tween  four  stationary  vanes,  V.  AVeights  were  attached  to 
cords  passing  over  the  pulley,  C,  and  wrapped  around  the 
roller,  A.  The  descent  of  these  weights  caused  the  wheel 
to  rotate.  The  box  was  filled  with  water  and  the  weights 
allowed  to  sink.  The  mechanical  work  expended  in  pro- 
ducing the  rotation  was  measured  by  the  descent  of  a  known 
weight  through  a  known  distance,  and  the  heat  was  deter- 
mined by  a  thermometer  at  T. 

After  allowing  for  all  sources  of  error,  and  repeating  the 
experiment  with  other  liquids,  and  with  iron  disks  sunk  in 
mercury,  Joule  found  that  the  quantity  of  heat  produced 
by  the  friction  of  bodies  is  always  proportioned  to  the  work 
expended. 

The  average  of  many  experiments  gave  772  foot-pounds 
as  the  mechanical  equivalent  of  the  heat  required  to  raise 
one  pound  of  water  1°  F.  Hence,  heat  and  mechanical 
force  may  be  exchanged,  one  for  the  other,  in  the  ratio  of 
772  foot-pounds  for  one  thermal  unit. 

625.  In  calculating  the  relation  between  mechanical  mo- 
tion and  heat,  all  the  possible  factors  must  be  found  and 
allowed  for,  in  order  to  obtain  the  exact  equivalence. 
When  a  body  falls  freely  through  the  air,  a  portion  of  its 
force  will  be  expended  by  friction  of  the  air,  and  the  heat 
produced  will  be  dissipated  by  radiation. 

If  a  body,  falling  through  a  vacuum,  is  suddenly  arrested 
by  collision  with  another,  the  heat  generated  will  be  in 
proportion  to  the  height  of  the  fall.  A  portion  of  this  heat 
may  bo  airain  instantly  converted  into  the  mechanical 
motion  of  the  rebound,  and  the  remainder  will  be  divided 
I. ctwccn  the  two  bodies.  Now,  since  the  height  through 
which  a  body  falls  is  proportioned  to  the  square  of  the 
velocity  attained  (V  =  8.02|/H),  the  heat  <r<-iierated  by 
the  percussion  of  bodies  moving  in  any  direction  will  be  as 
the  squares  of  their  velocities  at  the  time  of  impact. 

A  max  i.f  water,  falling  one  second,  attains  a  velocity  of  tliirtv-two 
feet,  and  <.i.  -trikin-  the  Around  would  generate  sufficient  ln-nt  to 


DYNAMICAL    THEORY.  353 

raise  its  temperature  7V65  °f  a  degree,  Fahrenheit,  if  the  heat  could 
all  be  concent rate<l  in  itself. 

The  temperature  attained  by  other  bodies  would  vary  with  their 
specific  heats:  thus,  a  leaden  bullet,  under  the  same  circumstances, 
would  be  raised  *-%?=*%  °  F.,  or  nearly  0°.64  F.  With  forty  times 
this  velocity,  it  would  generate  sixteen  hundred  times  as  much  heat; 
hence,  if  a  rifle  bullet  strikes  a  target  with  a  velocity  of  twelve  hun- 
dred and  eighty  feet  per  second,  it  will  generate  an  amount  of  heat 
sufficient,  if  concentrated  in  the  bullet,  to  raise  its  temperature  1024° 
F.  Tli is  heat  would  be  more  than  enough  to  fuse  the  bullet. 

626,  If  we  know  the  weight  and  velocity  of  any  moving 
body,  we  can  calculate  the  heat  which  would  be  generated 
by  suddenly  stopping  it.     Thus,  if  the  earth  were  stopped 
in   its  orbit,  it  would  develop  heat  equal  to  that  derived 
from  the  combustion  of  fourteen  equal  sized  globes  of  coal. 
If,  then,  it  should  fall  into  the  sun,  it  would  generate  heat 
by  the  collision  equal  to  that  evolved  by  the  combustion  of 
five  thousand  six  hundred  equal  worlds  of  solid  carbon. 

From  these  considerations,  it  is  thought  that  the  main- 
tenance of  the  solar  heat  is  due  to  the  falling  of  meteoric 
masses  into  the  body  of  the  sun.  The  maximum  velocity 
which  it  is  possible  that  such  a  body  can  attain  is  three 
hundred  and  ninety  miles  per  second.  With  this  velocity 
an  asteroid  striking  the  sun  would  develop  more  than  nine 
thousand  times  the  heat  generated  by  an  equal  asteroid  of 
solid  coal.  If  the  earth  should  strike  tiie  sun,  the  heat 
developed  by  the  shock  would  be  sufficient  to  supply  the 
solar  radiation  for  a  century. 

627.  The  dynamical  theory  also  explains  the  evolution 
and  consumption  of  heat  which   accompany  changes  in  the 
volume  or  state  of  bodies. 

Thus,  when  heat  enters  a  body,  its  actual  energy  is  ab- 
sorbed (1.)  in  increasing  the  intensity  of  molecular  motion, 
which  is  shown  by  a  rise  in  the  temperature;  (2.)  in  sepa- 
rating the  molecules,  as  shown  by  expansion,  and  (3.)  in 
re-arranging  its  molecules,  or  causing  a  change  of  condition. 
The  work  performed  is  partly  internal  and  partly  external, 
x  P.  23. 


354  NATURAL   PHILOSOPHY. 

The  exterior  work  is  employed  in  overcoming  external 
forces  which  resist  the  expansion,  and  the  interior  work  is 
employed  in  separating  and  re-arranging  the  molecules 
within  the  mass  of  the  body,  by  overcoming  cohesion  or 
affinity, 

628.  In  whatever  way  we  view  it,  the  interior  work 
performed  by  heat  is  enormous. '  Thus,  in  expansion,  a 
slight  rise  in  temperature  will  produce  a  dilatation  which 
would  require  the  expenditure  of  tremendous  mechanical 
power. 

Latent  heat  is  merely  a  consumption  of  heat  propor- 
tionate to  the  interior  work  required  to  overcome  cohesion 
in  melting  or  vaporizing  a  body.  The  heat  required  to 
melt  a  pound  of  ice  is  one  hundred  and  forty-three  thermal 
units,  which  is  equivalent  to  110396  foot-pounds.  The  heat 
required  to  change  boiling  water  into  steam  is  967  units, 
which  is  equivalent  to  746524  foot-pounds.  The  actual 
energy  of  the  heat  may  thus  be  measured  by  its  equivalent 
of  mechanical  motion.  Inasmuch  as  this  motion  may  be 
anain  transformed  into  sensible  heat  by  a  contrary  change 
of  state,  the  atoms  are  said  to  possess  a  possible,  or  potential 
energy. 

Thus,  when  a  gas  is  liquefied  by  compression,  external 
work  is  supplied,  and  the  interior  work  due  to  the  cohesive 
force  which  draws  the  molecules  together  is  transformed  into 
M-n>ible  heat.  In  like  manner,  the  cohesive  force  which 
changes  a  liquid  to  a  solid,  performs  interior  work,  and 
the  potential  energy  becomes  actual;  that  is,  the  latent  heat 
become.-  -en-ihlc. 

So,  also,  when  two  bodies  unite  by  chemical  affinity,  the 
molecular  motion  is  transformed  to  heat.  Thus,  when  -J-  of 
a  pound  of  hydrogen  combines  with  *  of  a  pound  of  oxviieii 
-.IK-  pound  of  .-team  is  produced,  and  o'S!)2  thermal  units 
are  evolved,  which  are  equivalent  to  ~>:}'2(H\'2\  foot-pounds. 
The  molecular  force  evolved  in  chaii^iiiu  n  mixture  of  these 
gases  in  a  pound  of  ice  will  therefore  be: 


CONSERVATION  OF  FORCE.  355 

Thermal  units.  Foot-pounds. 

1.  The  potential  energy  of  combination 6892  5320624 

±  The  potential  energy  of  steam 967  746524 

:;.  The  potential  energy  of  water 143  110396 

Total  energy 8002  6177544 

This  is  equivalent  to  the  force  required  to  raise  one  ton 
to  a  height  of  3098  feet,  or  3098  tons  one  foot  high. 
Molecular  forces  are,  therefore,  by  far  the  most  powerful 
of  any  with  which  we  are  acquainted. 

629.  Force  may  be  changed  but  not  annihilated.  The 
sun  is  the  ultimate  source  of  the  available  forms  of  force 
with  which  we  are  surrounded.  Let  us  consider  a  few  of  the 
ways  in  which  sunshine  may  be  transmuted  and  preserved: 

1.  The  mechanical  energy  of  the  winds,  of  falling  water, 
and  of  running  streams,  is  due  to  the  joint  action  of  gravi- 
tation and  the  solar  heat.     A  part  of  this  energy  may  be 
made  to  re-appear  as  heat  by  friction.     Thus,  a  large  room 
has  been   warmed  by  the  friction   of  two  plates,  made  to 
revolve  by  machinery  driven  by  a  fall  of  water. 

2.  Plants  grow   by  reason  of  the  light  and  heat  of  the 
sunshine,  and  accumulate  a  supply  of  fuel  and  food. 

(a).  Wood  and  mineral  coal  are,  therefore,  transmuted 
sunshine.  In  combustion,  the  solar  energy  again  appears 
as  heat,  or  may  be  applied  as  a  moving  force  for  engines. 

(6).  Food  is  transmuted  by  animals  into  animal  heat  and 
muscular  energy.  Beef  and  mutton  are,  therefore,  due  to 
solar  rays,  twice  transmuted. 

630.  Recapitulation, 

The  sources  of  heat  are, 

/-The  sun. 
1.  Physical  J  The  fixed  stars. 

v  The  molecular  forces. 
-.  ( 'lic'inical Combustion. 

f  Compression. 
:).  Mechanical -I  Percussion. 

(.  Friction. 


356  .V.  1  T  URA  L   PHIL  OSOPJI Y. 

THE    STEAM    ENGINE. 

631.  The  steam  engine  is  a  machine  in  which  the  elastic 
force  of  aqueous  vapor  is  the  motive  power.  The  essential 
parts  are  (1.)  the  boiler,  in  which  the  vapor  is  formed,  and 
(2.)  the  cylinder,  in  which  the  elastic  force  is  applied. 
Besides  these,  there  are  usually  other  contrivances  for  trans- 
ferring, regulating,  and  economizing  the  motion  which  is 
produced. 

Dr.  Wollaston's  glass  model  illustrates  the  action  of  the 
atmospheric  engine.  Fig.  283. 

To  the  boiler,  B,  is  attached  a  cylinder,  C,  in  which  a  piston,  P, 
works  steam  tight.  The  piston  rod  is  hollow,  and  is  closed  1>\  ;i 
screw  at  H.  The  boiler  is  first  partially  filled  with  water,  the  screw, 
H,  removed,  and  the  piston  forced  down  to  the  bottom  of  the 
cylinder. 

Heat  is  then  applied,  and  as  soon  as  the  steam  begins  to  escape 
from   the   piston   rod,  the  screw  is   replaced  on  the  top  of  the  rod. 
The  tension  of  the  confined  steam  will  then  force  the  piston  to  the 
top  of  the  cylinder.     Now,  if  the  cylinder  be  cooled  by  pouring  upon 
it  a  stream  of  cold  water,  a  partial  vacuum  will  be  formed 
within    it,   by    the   condensation   of  the    steam,    and    the 
piston  will  be  driven  down  by  the  pressure  of  the  atmos- 
phere. 

By  successively  heating  and  cooling  this  instrument,  ;m 
alternating,  or  up  and  down  motion,  will  be  communicated 
to  the  piston.  If  the  piston  be  made  to  perform  work 
by  connecting  it  with  suitable  machinery,  we  shall  then 
have  the  essential  action  of  Newcomerfs  engine. 

632.  This  engine,  constructed  in  1715,  by 
Thomas  Newcomen,  was  the  first  in  which  an 

FI.;.  MS.  alternating  motion  was  given  to  the  piston.  It 
was  used  to  raise  water  from  the  coal  mines  in 

Knirland.      Its  structure  is  exhibited  in  Fig.  284. 

To  one  end  of  :i  walking  beam,  F  V,  \\:\<  attache.]  the  piston  rod, 
hi',  mid  to  the  other  the  pump  rod.  W  X.  Tli.-e  parts  were  so 
CMimterl.alanced  that  the  weight  of  the  pump  rod  was  capaMe  of 
rai-iiiL'  ilie  pi-ton  to  the  top  of  th<-  cylinder.  Steam  was  then  ad- 
mitted to  the  cylinder  tlin.uL.|i  the  valve,  /,  and  the  air  was  allowed 
to  escape  through  the  eduction  valve,  E. 


NfJ  W  CO  MEN'S  ENGINE. 


357 


A-  -non  as  the  cylinder  was  filled  with  steam,  the  valves  E  and  i 
were  closed,  and  a  jet  of  cold 
water  was  injected  through  the 
valve,  t,  from  the  reservoir,  R. 
I)y  tli is  means  the  steam  was 
condensed,  and  a  partial  vacuum 
produced  beneath  the  piston. 
The  pressure  of  the  atmosphere 
then  forced  the  piston  down 
and  drew  up  the  pump  rod  at 
the  other  end  of  the  beam. 
The  jet  of  cold  water  was  then 
shut  off,  the  condensed  steam 
drawn  out  through  E,  fresh 
steam  re-admitted,  and  the  pro- 
cess was  continued. 

Humphrey  Potter  devised  an 
automatic  apparatus  by  which 
the  engine  opened  and  shut  its 
own  valves  at  the  proper  mo- 
ments. 

A        I 

633.  The    safety   valve, 

invented  by  Denis  Papin,  in  1690,  is  a  necessary  part  of 
every  steam  boiler.  This  consists  of  a  valve,  V,  fitting  an 
opening  in  the  top  of  a  boiler. 

A  lever  of  the  second  kind  rests 
above  this,  and  holds  it  in  its  place 
by  a  load,  M.  This  load,  which 
should  never  be  equal  to  the  full 
strength  of  the  boiler,  is  sometimes 
applied  to  the  lever  by  means  of 
springs.  Any  excess  of  this  tension 
will  be  shown  by  the  escape  of  the 
steam  from  the  valve.  In  the  recent  form,  shown  in  Fig.  285,  the 
small  orifices  at  t  are  filled  with  an  alloy  of  lead  and  bismuth. 

As  the  relation  between  the  temperature  and  tension  of  steam  is 
known,  the  fusing  point  of  the  alloy  is  made  less  than  the  tempera- 
ture of  steam  at  its  greatest  allowable  tension.  At  higher  tensions, 
the  alloy  will  melt  and  the  steam  escape.  Practically,  the  safety 
valves  are  only  indicators  of  high  tension,  as  the  openings  are  never 
large  enough  to  permit  much  steam  to  escape. 


FIG.  285. 


358 


NATURAL   PHILOSOPHY. 


634.  The  modern  steam   engine   is  due  to  James  Watt. 
In  1  "Go,  Watt,  while  engaged  in  repairing  a  model  of  New- 
comen's  engine,  devised  a  series  of  contrivances  for  obvi- 
ating its  defects,  and  between  that  time  and  1784  invented 
the  single  and  double  acting  steam  engines.     The  improve- 
ments added  by  others,  relate  chiefly  to  the  details  of  the 
mechanism.     The    following  are   the   principal    of   Watt's 
inventions : 

1.  The  condense)-.     This  is  a  chamber  (I,  Fig.  286),  into  which  the 
steam  from  the  cylinder  and  a  jet  of  cold  water  are  admitted  at  the 
same  time.     The  vacuum  is  formed  here,  and  avoids  the  loss  of  heat 
consequent  on  cooling  the  cylinder. 

2.  The  jacket.     This  is  simply  an  exterior  casing  of  wood,  to  pre- 
vent the  cylinder  from  losing  heat  by  radiation. 

3.  The  single  acting  engine.     Watt  admitted  the  steam  at  the  top  of 
the  cylinder,  and  thereby  depressed  the  piston  by  the  elastic  force  of 
the  steam  instead  of  by  the  weight  of  the  air. 

635.  These  improvements  changed  the  engine  from  an 
atmospheric   to  a  steam  engine.     The  piston  was  still  raised 

by  the  weight  of  the  pump 
rod,  and  consequently  the 
steam  acted  only  intermit- 
tently. These  single  acting 
engines  are  now  used  only 
for  pumping  water. 

4.  In  1782,  Watt  pat- 
ented the  double  acting 
steam  engine.  In  this,  the 
top  and  bottom  of  the  cyl- 
inder are  alternately  con- 
nected both  with  the  steam 
pipe  and  the  exhaust  pipe. 

The  theoretical  action  of  the 
condensing  engine  is  shown  in 
!'!•_•.  -JSU.  //  .-mil  I,  are  the  upper 

and   lower   valve-    of  the    steam    pipe;     K,  the   exhaii-t    pipe,    with    its 
',  '/;    and    I    the  conden.-er,   full  of  cold   water. 


WATT'S  STEAM  ENGINE.  359 

Now,  suppose  all  parts  of  the  cylinder  and  the  connecting  pipe  to 
be  filled  with  steam,  the  valves  a  and  c  to  be  opened,  and  b  and  d 
closed;  the  steam  will  pass  from  below  the  piston  through  the  ex- 
haust pipe  into  the  condenser,  and  thereby  a  vacuum,  more  or  less 
perfect,  will  be  formed  below  the  piston. 

The  steam  from  the  boiler  will  drive  the  piston  to  the  bottom  of 
the  cylinder.  When  the  piston  has  reached  its  lowest  point  the 
valves  are  changed;  that  is,  6  and  d  are  opened,  and  a  and  c  shut. 
Now,  a  vacuum  will  be  formed  above  the  piston,  steam  will  enter 
below,  and  the  piston  will  ascend. 

The  non-condensing  engine  differs  from  this  simply  in  the 
tact  that  the  waste  steam  passes  from  the  exhaust  pipe 
directly  into  the  air  or  into  the  smoke  stack  of  the  boiler. 
Fig.  287  is  a  condensing  engine.  The  locomotive,  Fig.  290, 
is  a  non-condensing  engine. 

5.  Tlie  parallel  motion.     This  was  a  device  to  make  the 
piston   rod  move  vertically  in  its  collar,  and  thus  prevent 
wear  and  friction.     Fig.  287. 

This  was  effected  by  a  system  of  jointed  rods,  A  B,  B  F,  F  D,  at- 
tached to  the  rod,  A  O,  moving  about  a  fixed  point,  O.  The  lengths 
«.f  these  rods  are  so  proportioned  that,  while  the  end  of  the  beam 
describes  an  arc  of  a  circle,  the  point,  B,  moves  in  a  very  nearly  ver- 
tical line.  This  is  also  true  of  the  center  of  the  link,  A  D,  to  which 
is  attached  the  pump  rod  of  the  hot  well. 

In  this  country,  the  piston  rod  is  generally  attached  to  a  cross 
piece,  which  moves  in  the  vertical  grooves  of  a  stiff  framework. 

6.  Tlie  crank.     The  motion  of  the  beam  was  transmitted 
through  the  connecting  rod,  F'M,  to  the  crank,  M  O',  which 
is  attached  to  the  shaft  of  the  engine,  and  gives  motion  to 
the  machinery  connected  with  it.     This  converts  the  alter- 
nating motion  of  the  piston  to  a  rotary  motion. 

7.  The  fly  wheel.     When  the  crank  is  at  its  highest  or 
lowest  position   the   steam   has   no  power  to  move   it,   and 
therefore  these  points  are  called  dead  points.     To  carry  the 
crank  beyond  these  points,  a  heavy  fly  wheel,  V  V,  is  attached 
to  the  shaft. 

This   wheel,    having   once  been   set  in   motion,  carries  the  crank 


360 


.V.  1  777,'. I  /.    rillL  OSOPIIY. 


beyond  the  dead  points  by  its  inertia,  and  brings  it  into  a  position 
where  the  power  again  becomes  effective. 

A  steamboat  or  locomotive  has  no  fly  wheel,  because  its  momentum 
is  sufficient  to  prevent  arrest  of  motion  at  the  dead  points. 

8.  The  throttle  valve,  T,  is  placed  in  the  throat  of  the 
steam  pipe  to  regulate  the  supply  nf  steam  to  the  cylinder. 
To  make  this  automatic,  Watt  applied  the  already  discovered 
principle  of  the  governor. 


Fi.;.  287. 

This  consists  of  a  vertical  axis,  y,  which  receives  from  the  shaft  ;i 
revolving  motion.  Attached  to  this  arc-  two  rods,  «&,«"//,  terminat- 
ing in  hravy  balls,  zz' ';  at  the  points,  bl/,  arc  applied  two  other 
n.d-,  he,  6/e/,  which  are  connected  with  a  collar,  m,  capable  of  mov- 
ing up  and  down  on  tin  vertical  axis.  When  the  engine  i-  at  iv-t, 
the  ball-  haii'_r  nearly  vertical,  but  when  the  axis,  //,  is  turned  they 
are  thrown  outward  by  centrifugal  force.  This  rai.-e-  the  collar,  m, 


WATT'S    IMTROVEMENTS. 


361 


which  acts  upon  the  throttle  valve,  by  levers,  not  shown  in  the  figure, 
so  as  to  admit  a  greater  or  less  supply  of  steam. 

The  weight  of  the  balls  is  adjusted  so  as  to  regulate  the  supply  to 
the  required  speed  of  the  engine.  If  the  shaft  moves  too  rapidly, 
the  balls  are  thrown  out  and  the  throttle  valve  closes ;  if  too  slowly, 
the  balls  fall,  and  a  greater  supply  of  steam  is  introduced. 

636,  Other  inventions  were  added  by  Watt,  which  relate 
to  details  of  construction,  and  are  here  omitted.  In  Fig. 
286,  the  eduction  and  steam  pipes  are  represented  on  oppo- 
site sides  of  the  cylinder.  In  the  actual  engine,  the  cylin- 
der has  but  two  ports  for  the  alternate  admission  and  ejec- 
tion of  steam.  These  ports  are  controlled  by  valves  of  vari- 
ous forms  and  niuiies.  Those  shown  in  Fig.  287,  are  called 
the  long  D  valves.  The  short  D  valve  is  the  one  generally 
used  in  land  engines. 

This  arrangement  for  the  distribution  of  steam  is  shown  in  Fig. 
288.  The  steam  is  admitted  from  the  boiler  into  the  valve  chest  be- 
hind the  valve.  Below  the  valve  is  the  exhaust  port,  o,  which  leads 
sideways  to  the  air  or  to  the  condenser.  On  each  side  of  this  are 
the  cylinder  ports,  which  are  connected  by  curved  tubes  to  the  top 
and  bottom  of  the  cylinder. 

The  valve  is  made  to  close  the  exhaust  port 
and  one  of  the  cylinder  ports  at  the  same  time, 
by  means  of  an  eccentric  rod,  d,  attached  to  the 
shaft  of  the  engine.  In  Fig.  288  the  lower 
port  is  open  for  the  admission  of 
steam ;  the  upper,  is  connected 
with  the  exhaust  port  to  allow 
the  waste  steam  to  escape.  In 
Fig.  289,  this  condition  is  reversed, 
the  lower  port  being  closed,  and 
the  upper  open. 

Sometimes  a  second  valve, 
FIG.  2.v>.  called  a  "  cut  off,"  is  attached 

to  the  sliding  valve,  by  which        Fw 
the  steam  may  be  shut  off  from  the  cylinder  at 
any  portion  of  the  stroke  of  the  piston,  as  one-half  or  one- 
third.     The  expansion  of  the  steam  already  admitted  to  the 
cylinder  completes  the  work  of  moving  the  piston. 


362  \ATl'/fAL   PHILOSOPHY. 

637.  Steam  boilers  vary  in  shape  and  size  with  the  pur- 
pose for  which  they  are  designed.  In  locomotives,  an 
abundant  supply  of  steam  at  high  tension  is  required. 
For  this  reason,  the  boiler  is  pierced  with  numerous  hori- 
zontal pipes,  which  serve  as  Hues  for  the  fire,  and,  at  the 
same  time,  expose  a  large  heating  surface  to  the  water.  To 
increase  the  draft,  the  exhaust  pipe  is  placed  in  the  smoke 
stack. 


Fi.;.  290. 

638.  The  mechanical  power  of  steam  may  he  estimated 
in  foot-poimd>  or  in  horse-powers.  A  cubic  foot  of  water 
when  converted  into  steam  yields  Hi'.Hi  eiil.ie  li-et  at  the 
pre  — lire  of  one  aliiHisj.ln-rc.  Hence,  if  the  steam  he  formed 
beneath  a  pi>t..n  of  one  foot  area,  it  is  capable  of  lifting  a 
weight  of  fifteen  pound-  on  cadi  square  inch,  to  the  height 
<>f  I('»!M;  feet.  This  is  equivalent  to  rai>iiiL!  lf>Xl44X 

Him;      :;i;i;:;:;r,ii   i;..,t-poimds.     Deducting  one-iil'th    for   loss 

by    friction  and   other  CM1M6,   the  available   power  of  a  cubic, 


POWER    OF  STEAM.  363 

foot  of  water,  when  converted  into  steam  at  212°,  is  2930688 
foot-pounds. 

The  horse  powers  depend  on  the  rapidity  of  the  evapora- 
tion. If  the  boiler  evaporates  a  cubic  foot  of  water  each 
minute,  its  efficiency  will  be  equal  to  2930688  -f-  33000  = 
88.8  horse  powers.  In  rough  calculations,  it  may  be  as- 
sumed that  the  evaporation  of  one  cubic  foot  per  hour  is 
equal  to  one  horse  power. 

To  evaporate  one  cubic  foot  of  water  requires  the  com- 
bustion of  nearly  five  pounds  of  anthracite  coal.  Hence, 
for  each  pound  of  coal  burned  per  minute,  we  should  have 
an  effect  equal  to  nearly  twenty-five  horse  powers.  This  is 
very  nearly  realized  in  the  Cornish  single  acting  condensing 
engines.  In  the  United  States,  it  is  usual  to  allow  about 
6.5  pounds  of  anthracite  coal  for  each  horse  power. 

639.  Recapitulation. 

The  essential  parts  of  a  steam  engine  are : 

1.  A  boiler,  for  generating  the  elastic  force  of  steam. 

±  A  cylinder  in  which  this  elastic  force  is  made  to  produce  an 
alternating  motion  in  a  piston. 

The  accessory  parts  are : 

1.  An  apparatus  by  which  the  piston  rod  is  made  to  move  in  the 
same  straight  line.     (Parallel  motion). 

2.  An  apparatus  by  which  the  alternating  motion  of  the  piston 
may  be  converted  to  rotary.     (Crank.) 

3.  Apparatus  for  regulating  and  controlling  the  motion.     (Fly 
wheel,  throttle  valve,  and  governor.) 

4.  Other  parts  added  for  the  sake  of  safety,  economy,  and  con- 
venience.   (Safety  valve,  condenser,  jacket,  and  automatic  action.) 


364  NATURAL   PHILOSOPHY. 


CHAPTER   IX. 


640.  It  has   long  been  known  that  a  certain  ore  of  iron, 
called  the  loadstone,  has  the  remarkable  property  of  attract- 
ing iron  filings  to  itself:   also,  that  amber  when  rubbed,  and 
tourmaline  when  heated,  acquire  temporarily,  the  property 
of   attracting   light    bodies,    as    bits    of   cotton    and    straw. 
Within  the  past  century,  philosophers  have  found  that  these 
arc  but   particular  manifestations  of  a  force  which  is  con- 
stantly evoked  in  all  kinds  of  molecular  changes,  and  whose 
phenomena   are   among   the   most  wonderful   and   beautiful 
in   nature.      This  force  is  electricity.      It  is   convenient  to 
study  its  phenomena  under  three  divisions:   (1.)  magnetism, 
(2.)  statical  electricity,  (3.)  dynamical  electricity. 

MAGNETISM. 

641.  The  loadstone  is  an  abundant  and  widely  distributed 
ore  of  iron,  having  the  chemical  formula  Fe3O4.      Because 
the   ore   was   first    found    near   Magnesia,   a    city  of   Asia 

Minor,  loadstones  are  called  nnlnrnl 
magnets.  If  a  loadstone  be  rolled 
in  iron  filings,  the  filings  will  cling 
to  it,  but  especially  at  its  ends. 
Ki,;.  »i.  Fig.  291.  These  ends  are  termed 

the  poles  of  the  magnet.     The  force 
residing  in  a  magnet  is  called  magnetism. 

Artificial  magnets  are  bars  or  needles  of  hardened  steel 
which  have  acquired  magnetic  proper-tie.-.  These  are  at 
once  more  convenient  and  powerful  than  natural  magnet.-. 
If  a  magnetic  bar  or  needle  be  poised  at  it-  center  so  that 
it  will  -win-  t'n-ely.  one  end  will  always  point  toward  the 
north  and  the  other  toward  the  south.  Hence,  one  end  is 


MA  G  NET  ISM. 


365 


called  the  south  and  the  other  the  north  pole  of  the  magnet. 
The  north  pole  is  the  marked  end  of  the  magnet. 

If  a  sheet  of  stiff  paper  be  laid  upon  a  bar  magnet  and 
iron  filings  be  sifted  evenly  upon  the  paper,  the  particles 
of  iron  will  arrange  themselves  in  curved  lines  about  the 


FlO.  292. 

poles.  Fig.  292.  These  lines  are  called  lines  o/  magnetic 
force.  The  action  of  the  magnet  is  not  diminished  by  the 
interposition  of  any  substance  that  is  not  itself  magnetic, 
as  paper  or  glass. 

642.  Either  pole  will  equally  attract  magnetic  substances; 
but  if  two  magnets  are  brought  near  each  other,  it  will  be 
found  that  the  marked  end  of  one  will  attract  the  south 
pole  of  the  other,  but  if  the 

two  marked  ends  are  brought 
near  each  other,  a  repulsion 
takes  place.  Hence,  this  law : 
Like  poles  repel  aud  unlike 
poles  attract  each  other. 

A  force  which  exhibits  a 
combination  of  equal  powers, 
acting  in  opposite  directions, 
is  called  a  polar  force. 

643.  If  a  long  steel  needle 

be    magnetized,     the    center  FIG.  293. 

will   exhibit  no  magnetic  force,  and   is  said  to  be  neutral. 


366 


NATURAL    PHILOSOPHY. 


If  the  needle  be  broken,  each  half  will  be  found  to  be  a 
magnet  with  two  equal  and  opposite  poles.  If  this  division 
be  continued,  no  portion  can  be  obtained  so  small  that  it 
will  not  be  a  perfect  magnet.  We,  therefore,  conclude  that 
every  magnet  is  a  collection  of  polarized  particles,  having 
their  similar  poles  turned  in  the  same  direction. 

Thus,  if  N  S,  Fig.  294,   represents  a  magnet,  the  alternate  black 
and  white  spaces  will  represent  the  polarity  of  each  particle.     All  the 


n"  sf'  n'  sf  n  s 


Fio.  294. 

north  poles  are  disposed  in  one  direction  and  all  the  south  poles  in 
the  opposite.  The  opposite  polarities  balance  each  other  at  the  center, 
which  thus  remains  neutral,  but  are  strongly  manifested  at  the  ends. 

644.  Induction.  If  a  rod  of  soft  iron,  (Fe,)  Fig.  295,  be 
brought  near  one  of  the  poles  of  a  magnet,  M,  the  rod  will 
become  a  temporary  magnet,  having  two  poles,  each  capable 
of  attracting  iron  filings.  The  polarity  of  the  rod  will  be 
opposite  to  that  of  the  magnet;  that  is,  if  the  rod  be  near 


Ki.i.  •». 

the  marked  end  of  the  magnet,  the  nearer  end  of  the  rod 
will  manifest  south  polarity,  and  the  remote  end  north. 
This  influence,  by  virtue  of  which  a  magnet  can  develop 
magnetism  in  iron,  is  called  induction. 

The  phenomena  <>f  induction  may  be  explained  by  supposing  thai, 
in  the  omnagnetized  condition  of  the  rod,  all  the  molecules  are  en- 
dued with  magnet  i-m,  Imt  M  combined  that  the  opposite  forc< 

trali/e  e;ich  other.  In  the  presence  of  a  magnet  the  two  halves  of 
•  itch  moh-enle  as-miir  an  opposite  magnetic  condition,  or  become 

pnlari/ed.  M  -liown    in    FL'.   'JUl. 


MAGNETIC  SUBSTANCES. 


367 


645.  In   any  form   of  induction  there  is   no  transfer  of 
:uiy  force,  but  merely  a  development  of  polarity  among  the 
particles   of  the  body  acted   upon.     The  lines  of  magnetic 
force,  Fig.  292,  are  due  to  the  fact  that  the  minute  particles 
of  iron  become  temporary  magnets,  and  arrange  themselves 
in  accordance  with  the  law  of  attraction  and  repulsion. 

The  inductive  force  is  greatest  when  the  magnet  is  in  contact  with 
the  iron,  but  entirely  ceases  when  the  two  are  separated  to  a  sufficient 
distance.  If  a  steel  bar  be  in  contact  with  a  magnet,  its  particles  be- 
come polarized  very  slowly ;  but,  when  once  acquired,  its  magnetism 
is  permanent.  Magnetism  may  be  sooner  induced  in  steel  by  rubbing 
it  with  one  of  the  poles  of  a  magnet.  In  this  way  the  ordinary  mag- 
netic needles  are  prepared ;  but  the  most  powerful  magnets  are  pro- 
duced by  means  of  a  voltaic  current,  as  will  be  described  hereafter. 
(745.) 

646.  A  magnetic   battery  consists  of  a  number  of  mag- 
nets joined   together    with   their   similar  poles   in    contact. 
The  most  common  form  is  that  of  the  horse-shoe,  Fig.  296. 
When  a  magnet  exerts  its  inductive  power 

on  a  piece  of  soft  iron,  its  own  magnetic 
intensity  is  increased.  For  this  reason  the 
magnet  is  provided  with  a  keeper,  or  arma- 
ture, K,  of  soft  iron.  The  weight  which 
the  armature  will  support  is  more  than 
twice  that  which  either  pole  would  bear. 
The  power  of  a  magnet  may  be  doubled 
by  adding  daily  a  small  weight  to  the  ar- 
mature; but  if  the  contact  be  once  broken 
only  the  original  load  will  be  sustained. 
The  power  of  a  magnet  may  be  seriously 
impaired  by  heating,  or  by  any  rough 
usage. 

647.  Magnetic   substances  are  those  which  are  attracted 
by  a  magnet.     Iron,  steel,  nickel,  and  cobalt  are  the  only 
substances    in   which    magnetism   can    be  developed  by  or- 
dinary induction.     By  using  very  powerful  magnets,  Fara- 
day found  a  small  number  of  other  substances  to  be  mag- 


Fio.  2%. 


368 


NATURAL   PHILOSOPHY. 


netic.     Among  these  are  manganese,  chromium,  platinum, 
plumbago,  and  oxygen. 

On  the  other  hand,  a  great  number  of  substances,  when 
suspended  between  the  poles  of  a  strong  horse-shoe  magnet, 
take  up  a  position  at  right  angles  to  the  line  joining  the 
poles,  as  if  repelled  by  them.  Such  substances  are  called 
diamagnetic.  Among  diamagnetic  substances  are  phos- 
phorus, bismuth,  antimony,  zinc,  tin,  resin,  hydrogen,  and 
coal  gas. 

TERRESTRIAL    MAGNETISM. 


648.  If  a  small  magnetic  needle  be  suspended  by  an 
untwisted  thread  over  a  bar  magnet,  N  S,  and  be  slowly 
carried  from  one  end  of  the  bar  to  the  other,  it  will  assume 
in  succession  the  positions  shown  in  Fig.  297.  At  the 
center  of  the  bar  it  will  be  horizontal,  with  its  marked  end 
pointing  toward  the  south  pole  of  the  bar  magnet.  At 
either  side  of  the  center,  it  dips  or  inclines;  the  south  pole 
dips  on  the  north  polar  side  of  the  center,  and  the  north 
pole  dips  on  the  south  side.  The  dip  will  increase  as  tin 


n, 
VII 

1 

VI 

f        v 

•V 

UL  \ 

II 

Fio.  297. 

aeedk  approaches  the  poles,  at  which  points  the  inclination 

will  be  <)0°. 

Now,  if  a  magnetic  needle  be  freely  suspended  and  car- 
ried to  different  points  on  the  earth's  -nrf'arc,  it  will  not 
nicrdy  l»e  directed  toward  the  north,  lmt  will  also  dip  more 
and  mure  a-  it  approaches  the  polar  regions.  These  phenom- 
ena warrant  u>  in  r.iii^idmnir  the  earth  as  a  great  magnet, 
who.-e  poles  are  very  near  the  t»-m->trial  poles. 


MAGNETIC  ELEMENTS. 


369 


649.  The   magnetism  of  the  earth  is  further  manifested 
l»v  its   inductive   influence.     If  a   bar  of  iron   be  placed  in 
[In-  direction  which   a  dipping  needle  would  assume,  it  im- 
mediately becomes  polarized. 

This  may  be  shown  by  moving  a  small  magnetic  needle  along  the 
bar.  The  marked  end  of  the  needle  will  be  repelled  by  the  lower  end 
of  the  bar,  and  attracted  by  its  upper  end.  If  the  iron  is  somewhat 
hard,  its  magnetism  may  sometimes  be  rendered  permanent  by  strik- 
ing it  a  sharp  blow  with  a  hammer.  This  phenomenon  is  frequently 
seen  in  rods  which  remain  at  rest  for  some  time  in  a  nearly  vertical 
position,  as  the  poker  and  tongs. 

650.  The  magnetic  elements  necessary  for  the  full  knowl- 
edge of  the  earth's  magnetism  at  any  place,  are  (1.)  incli- 
nation, (2.)  declination,  (3.)  intensity. 

Inclination.  If  an  unmagnetized  steel  bar  be  accurately 
balanced  and  then  magnetized,  it  will  be  found  that  its  bal- 
ance is  lost,  and  that  it  now  makes  a  certain  angle  with  the 
horizon.  This  angle  is  called  the  inclination,  or  dip,  of  the 
needle.  A  dipping  needle,  is  one  by  means  of  which  this  incli- 
nation can  be  measured. 
The  inclination,  N  cd, 
shown  in  Fig.  298,  is  the 
same  as  that  of  a  dipping 
needle  at  Rochester,  N. 
Y.,  or  about  75°. 

651.  The    magnetic 
poles  are  points  at  which 
the    dipping    needle    is 
vertical.    Sir  James  Ross 
found  an    inclination   of 
89°59'  in  Boothia  Felix, 
at  70°o'  N.  lat.  and   96° 

43'  W.  Ion.  This  point  is  taken  as  the  north  magnetic  pole. 
The  south  ma.irm-tic  pole  is  calculated  to  be  in  about  75°30' 
S.  lat.,  and  154°  E.  Ion.  Lines  connecting  places  in  which 

N.  P.  24. 


Flo. 


370  NATURAL  PHILOSOPHY. 

the  needle  is  of  equal  dip  may  be  drawn  about  the  mag- 
netic poles  in  irregular  curves,  somewhat  resembling  those  of 
the  parallels  of  latitude  drawn  about  the  terrestrial  poles. 
Most  of  the  United  States  lies  between  the  lines  of  75°  dip 
and  60°  dip.  The  mcujmtir  cijmttor  of  the  earth  is  a  line  of 
no  dip,  or  it  is  a  line  connecting  those  places  in  which  the 
needle  remains  horizontal.  The  magnetic  equator  crosses 
the  earth's  equator  in  the  Atlantic  and  Pacific  oceans. 
making  an  angle  with  it  of  about  12° 

In  the  northern  hemisphere,  the  marked  end  of  the  needle  is  <U-- 
pressed,  and  in  the  southern,  the  unmarked  end.  In  the  mariner's 
compass,  the  effect  of  the  dip  is  corrected  by  the  means  of  a  small 
sliding  weight,  which  is  moved  along  the  needle  so  as  to  preserve  its 
equilibrium. 

652.  Declination.     Since  the  magnetic  poles  do  not  coin- 
cide with  the  terrestrial  poles,  the  needle,  in   most  places, 
does  not  point  in  a  true  north  and  south  line.      The  angle 
by    which    its    direction     deviates    from     the    astronomical 
meridian   is  called   the  declination  of  the  needle.     The  com- 
pass,  Fig.   299,   may   be    used    to  determine  the  declination 

by  observing  the  angle  which 
the  needle  makes  with  the 
direction  of  the  north  polar 
star.  The  declination  is  fre- 
quently called  the  variation 

of    tin     ro///y^/ss,     because     it     is 

generally  different  for  differ- 
ent places.  It  is  0°  at  Pitts- 
burgh, <i°  west  at  New  York, 
and  in  I>afiin's  Hay  the  needle 
Fig.  299.  points  due  west. 

653.  A    line    of  no    declination,    or   one    that    connects 
places    in    which    the    needle    points    due    north    and    south, 
passes    in    nearly    a    great    circle    around    the    globe.       In    the 
\\vstcrn    hemisphere    it    runs    from    the    north    magnetic    pole 
through   Hudson's    P»ay  and    Lake    Kric,  cutting  Ohio,  Penn- 


MAGNETIC  INTENSITY.  371 

svlvania,  Virginia,  and  North  Carolina,  and  enters  the 
Atlantic  near  Cape  Lookout;  thence  it  sweeps  eastward  of 
the  West  Indies,  and  after  passing  through  the  south  polar 
regions,  re-appears  at  tin-  south  magnetic  pole.  It  then 
runs  northerly  through  Australia,  but  beyond  this  follows 
an  irregular  curve  through  the  Caspian  sea  to  the  Arctic 
ocean. 

In  the  Atlantic  hemisphere,  which  is  included  within  this  line,  the 
deviation  is  every-where  westward.  In  the  Pacific  hemisphere,  which 
includes  the  greater  part  of  the  United  States,  the  declination  is  very 
generally  eastward ;  the  exception  being  an  oval  area  in  Eastern  Asia, 
which  is  bounded  by  a  second  line  of  no  declination. 

654.  Intensity.      If  a  magnetic  needle   be  drawn   aside 
from   its  position   of  rest,   it  will   recover  its  equilibrium 
after  a  series  of  oscillations.     Since  the  magnetic  force  at 
any  given   place   and   time   may  be   regarded   as   constant, 
these  oscillations  of  the   needle  will   be   governed  by  laws 
analogous    to    those    of    the    pendulum.       [41    and    42.] 
Hence,  the   intensity  of  the  earth's  magnetism  in  any  two 
places,  will  be  proportioned  to  the  square  of  the  number  of 
vibrations  made  by  the   same   needle   in  equal   times.     The 
magnetic  intensity  in  Peru  has  been  assumed  as  the  stand- 
ard of  comparison,  and  is,  therefore,  taken  as  unity. 

A  dipping  needle,  which,  in  Paris,  made  245  vibrations  in  ten  min- 
utes, when  transported  to  the  magnetic  equator  in  Peru,  made  only 
211  vibrations  in  the  same  time.  The  intensity  at  Paris  will,  there- 
fore, be  ^  =  1.348. 

655.  There  are  four  foci  of  maximum  magnetic  intensity, 
of  which  two  are  in  the  northern  and  two  in  the  southern 
hemisphere.      The   strongest,    which   lies   a   little   south   of 
Australia,    may  be   represented    by   2.06.      The   American 
focus  lies  a  little  north-west  of  Lake  Superior,  the  intensity 
being  1.88.     The  least  intensity  hitherto  found  is  in  South 
Africa,    and    aim  units    to    0.7,   or  about   one-third    of   the 
highest  intensity. 


372  NATURAL   PHILOSOPHY. 

The  absolute  magnetism  of  the  earth  lias  been  raleulated  to  be  equal 
to  eight  thousand  lour  hundred  and  sixty-four  quadrillion  times 

that  of  a  saturated  bar  magnet  one  pound  in  weight. 

656.  The  magnetic  elements  are  subject  to  constant 
changes,  some  of  which  are  regular,  and  others  irregular. 
Thus,  the  inclination  in  Europe  is  gradually  decreasing, 
and  the  declination  is  at  present  veering  eastward.  The 
rate  of  these  changes  is  not  the  same  for  different  places, 
nor  is  it  constant  for  the  same  place.  The  following  list 
exhibits  the  secular  changes  in  declination  and  inclination 
at  London : 

Table  of  Secular  Magnetic  Changes. 


Y.ar. 

1")8() 

Declination. 

11017XE 

Y«-ar. 

1720  

Inclination. 

74°4>)/ 

HifiO 

0°  O7 

1790 

71°53X 

1815 

040.);'  w 

1818     

70°34/ 

18fi9... 

...20°  2'W. 

1869  .. 

...67°54' 

It  appears  from  this,  that  in  1660  the  needle  pointed  due  north,  at 
London;  it  then  varied  westward  until  1S1.~>.  when  it  pointed  farthest 
from  the  true  north.  Since  that  time  it  has  moved  eastward  at  an 
annual  rate  of  about  8'.  The  annual  decrease  in  dip  is  about  2'.6. 

657.  These   changes   show  that   the  magnetic  poles   are 
continually  shifting   their    position,  and,  consequently,  that 
the  lines  of  equal   declination   and  dip  are   not  the  same 
from  year  to  year. 

The  needle  has  also  a  daily  and  annual  oscillation,  ap- 
parently connected  with  changes  in  temperature.  Thus,  at 
Philadelphia  it  has  a  maximum  westward  declination  at 
1  P.  M.  and  at  2  A.  M.,  and  a  minimum  at  ft  A.  M.  and 
at  10  P.  M.  The  greatest  daily  change  is  between  April 
ami  September,  or  during  the  summer  months. 

658.  The   irregular  variations   an-   indicate.!   by  sudden 

di-tiirbam-i's  «>f  the  magnetic  needle,  which  are  x.niet  iine> 
con-iderable,  but  are  of  short  duration.  The  appearance  of 
the  Aurora  l>oreali>  is  invariably  accompanied  by  these 


STATICAL    ELECTRICITY.  373 

fluctuations.  Magnetic  disturbances  often  occur  simultane- 
ously in  very  distant  countries,  and  have  received  the  name 
of  magnetic  storm*. 

These  storms,  which  were  once  thought  to  be  wholly  irregular, 
are  found  to  be  periodical,  having  epochs  of  maximum  intensity 
every  ten  years.  These  epochs  coincide  with  the  maximum  recur- 
rence of  the  spots  on  the  sun;  this  appears  to  show  that  magnetic 
storms  are  connected  with  changes  in  the  solar  atmosphere. 

659.  The  source  of  the  earth's  magnetism  is  now  gen- 
erally attributed  to  the  sun.  It  is  supposed  that  the  solar 
heat  develops  electrical  currents  in  the  materials  of  the 
earth's  surface,  and  that  these  currents  give  rise  to  mag- 
netic phenomena.  This  hypothesis  is  supported  by  the 
facts  already  noticed  in  regard  to  magnetic  storms,  and  the 
daily  changes  in  declination,  and  receives  a  strong  support 
from  the  fact  that  the  lines  of  equal  beat  and  of  equal 
magnetic  intensity  on  the  globe,  manifest  a  marked  corre- 
spondence. 

660.  Recapitulation. 

Magnets  are  .........  {  Natural  or  artificial. 

I  Permanent  or  temporary. 

Subst-inces  ("Attracted  by  magnets  are  ..........  Magnetic. 

I-  Repelled  by  magnets  are  ..........  Diamagnetic. 

{Inclination. 
Declination. 
Intensity. 

,  Daily. 
The  changes  of  the  magnetic  ele-  f  Re8ular-  Annual. 

(  Secul:ir' 


mentsare  ........................... 

v  Periodical,  in  magnetic  storms. 


STATICAL    ELECTRICITY. 

661.  The  fundamental  phenomena  of  statical  electricity 
may  be  studied  by  means  of  the  electric  pendulum,  Fig.  300. 
This  consists  of  a  pith  ball  attached,  by  means  of  a  silk 
thread,  to  a  glass  support. 


374 


NA  TURA  L    PHIL  OS OJ'/f  } '. 


Flo.   300. 


If  a  stick  of  sealing  wax,  or  an  ebonite  ruler  be  rubbed  with 
dry  llainu'l  and  be  brought  near  the  pith  ball,  the  latter  is  in- 
stantly attracted  but  is  soon  re- 
pelled. If,  now,  a  warm  glass 
rod  lie  rubbed  with  a  silk  hand- 
kerchief, and  presented  to  the 
ball,  the  same  phenomenon  of 
attraction  and  repulsion  will  be 
observed  Fig.  300. 

It  will  now  be  found  that  when 
the  hall  has  been  repelled  by  tin- 
glass,  it  will  be  attracted  by  the 
wax ;  and  when  again  repelled 
by  the  wax,  it  will  be  attracted 
by  the  glass.  If  the  glass  and 
wax  be  placed  on  opposite  sides 
of  the  ball,  it  will  vibrate  between 
them  by  the  alternate  attraction 
and  repulsion  of  each.  It  is, 

therefore,  manifest  that  the  excited  glass  and  wax  manifest  similar  but 
opposite  properties.  These  properties,  thus  developed  by  friction,  are 
due  to  the  force  of  electricity. 

662.  Electricity  is  a  polar  force  which  becomes  manifest 
by  its  peculiar  phenomena  of  attraction  and  repulsion.     It 
is  now  regarded  as  a  mode  of  molecular  motion,  which  is 
always  manifested  in  two  opposite  or  polarized  states.    That 
developed  on  the  glass  is  called  positive  (-}-),  and  that  on 
the  wax  negative  electricity  ( — ). 

Formerly,  electricity  was  supposed  to  be  due  to  the  presence  of 
two  fluids,  called  vitreous,  or  jn^lfii-f,  and  resinous,  or  negative.  Many 
of  the  terms  of  the  older  theory  are  still  in  common  use,  because 
they  are  convenient  for  describing  most  electrical  phenomena,  al- 
though the  meaning  attached  to  them  is  taken  in  a  sense  different  from 
that  originally  intended.  There  is  no  evidence  of  the  existence  of 
any  electrical  fluid. 

663.  In  the  preceding  experiment,  we  suppose  that  the 
wax    became   negatively  elect rii'n-d    l»y   the   friction,    and,    on 
contact,  transferred  a  portion  of  this  force  to  the  hall.     The 
ball  thereby  became  electrified  or  rharyvd  with  negative  elec- 
tricity,  and    the    two    l»odi<--    >«-paruted.      On    bringing   the 


CONDUCTORS  AND   INSULATORS.  375 

charged  ball  near  the  positively  electrified  glass,  the  t\vo 
were  attracted  because  of  their  different  electrical  states. 
The  glass  then  communicated  enough  of  positive  electricity 
to  neutralize  the  negative  electricity  of  the  ball,  and  also  to 
render  it  positively  charged.  The  ball  was  then  repelled  by 
the  glass  and  attracted  by  the  wax,  and  so  on  through  a 
series  of  attractions  and  repulsions.  From  these  experi- 
ments we  derive  the  following  law:  Two  bodies  cliarged  witii 
like  electric  it  ir*  repel  eacJi  other;  two  bodies  charged  with  opposite 
fl<-Hricitit'4  attract  each  otJier. 

664.  Statical  electricity  may  be  developed  by  any  cause 
that  tends  to  disturb  the  'molecular  condition  of  bodies,  as 
cleavage,  pressure.     It  may  be  developed  in  tourmaline  and 
certain  other  minerals  by  heat.     The  usual  source  is  friction, 
and  hence  this  form  of  electrical  force  is  sometimes  called 
J'l'ictional  electricity.     It  is  called  statical  electricity  because 
it  may   te    retained   for  a   time  on  an  excited  or  charged 
body. 

665.  Electricity  is  transmitted  from  one  body  to  another 
with   different  degrees   of  rapidity.     Those   substances   that 
transmit  electricity  readily  are  called  conductors;  those  that 
do  not  are  called  non-conductors,  or  insulators. 

These  classes  differ  only  in  degree,  for  there  is  no  such  thing  as 
perfect  conduction  or  perfect  insulation.  In  the  following  list,  the 
substances  named  are  arranged  in  the  order  of  their  conducting 
power.  Those  midway  in  the  list  may  be  term  semi-conductors  or 
semi-insulators. 

Conductors.  Semi-conductors. 

1.  All  the  metals.  10.  Alcohol.  19.  Furs. 

2.  Charcoal.  11.  Ether.  20.  Silk. 

3.  Graphite.  12.  Flowers  of  sulphur.  21.  Gems. 

4.  Acids.  13.  Dry  wood.  22.  Glass. 
o.  Water.  14.  Paper.  23.  Wax. 

»i.  Vegetables.  15.  Dry  ice.  24.  Sulphur. 

7.  Animals.  16.  Phosphorus.  25.  Resins. 

8.  Linen.  17.  Caoutchouc.  26.  Shellac. 

9.  Cotton.  18.  Air  and  gases.  27.  Ebonite. 

Semi-iiisulators.  Insulators. 


:;TI;  NATURAL 

666.  In  order  that  a  charged  body  may  retain  its  elec- 
trical force,  it  must  either  be  a  non-conductor  or  be  insulated 
by  being  supported  on  non-conductors.     The  most  common 
insulators  are  made  of  green  glass ;    ebonite  is  the  best.  * 
Baked  wood  covered  with  shellac  varnish  will  answer  very 
well.     Dry  air  is  essential  for  insulation.     In  a  damp  room 
a  film  of  moisture  gathers  upon  the  apparatus  and  forms  a 
conducting  surface. 

The  reason  why  electrical  excitement  is  not  more  frequently  mani- 
fested by  friction  is  because  the  electrical  force  is  carried  off  as  fast 
as  it  is  developed.  When  the  electrical  force  is  sufficient  to  force  its 
way  through  a  bad  conductor,  a  spark  may  be  produced.  In  dry, 
frosty  weather,  a  person,  by  shuffling  about  a  warm,  carpeted  room 
in  dry  slippers,  may  develop  electricity  sufficient  to  emit  a  spark 
from  his  finger  capable  of  igniting  a  jet  of  gas. 

667.  Both  kinds  of  electricity  are  always  simultaneously 
produced.     If  two  insulated  disks  of  dry  wood,  one  covered 
with  shellac  and  the  other   with  silk,  are  rubbed  together 
and  separated,  the  shellac   will   manifest  positive  and  the 
silk   negative  electricity.     Any  substance  in  the  following 
list,  when  rubbed  by  any  one  succeeding  it,  becomes  posi- 
tively electrified,  and  by  any  one  preceding  it,  negatively 
electrified  : 

+  Cat's  fur,  flannel,  smooth  glass,  cotton,  paper,  silk,  the  hand, 
sealing  wax,  rough  glass,  sulphur,  ebonite — . 

Thus,  paper  becomes  negatively  electrified  when  rubbed  with  Haniu-1, 
and  positively  electrified  when  rubbed  with  silk. 

668.  An  electroscope  is  an  instrument  used  to  detect  the 
pn-.-rnee  and  determine  the  kind  of  electricity  in  any  body. 

The  simplest,  is  some  form  of  the  electrical  pendulum,  with  one 
or  two  pith  balls.  The  gold  Ira!'  eleet  ro-e.  ,pe.  Fi^.  .",01,  consists  of 
two  strips  of  gold  leaf  .-uspended  in  a  glass  vessel  by  means  of  ;i 
metallic  rod.  which  terminate.--  in  a  knob,  or  plate.  The  upper  por- 
tion of  the  jar  is  coated  with  >hellac  and  the  interior  is  filled 
with  air  kept  perfectly  dry.  Within  the  ve.-sel  are  two  metallic 


This  i>  tin-  material  ol  which  hard  rubber  combs  are  made. 


ELECTRICAL    INDUCTION. 


377 


i  serve  to  remove  an  excess- 


onnected  with  the  ground  whicl 
ive  charge  from  the  k-aves. 

If  the  knob  be  touched  with  an 
t/lertrilied  glass  rod,  the  leaves 
will  diverge,  because  they  become 
charged  with  positive  electricity. 
If,  now,  any  electrified  body  be 
brought  near  the  knob,  the  kind 
of  electricity  in  the  body  may  be 
determined  by  its  influence  on  the 
leaves ;  for  if  the  electricity  be  of 
the  same  kind  as  that  of  the 
leaves,  they  will  diverge  farther, 
lint  if  of  the  opposite  kind,  they 
will  collapse. 

669.  Induction.  Electri- 
fied bodies  influence  bodies 
at  a  distance  in  a  manner 
analogous  to  the  action  of  a  FIG.  301. 

magnet    on     magnetic     sub- 
stances.    This  influence  is  called  electrical  induction,  and  the 
resulting  effect  induced  electricity. 

Let  A  B  be  a  conductor  of  brass  or  tin,  insulated  on  a  glass  pillar 
and  furnished  with  a  number  of  pith  ball  electroscopes.     If  this  is 


FIG.  302. 


brought  near  an  electrified  body,  C,  but  without  receiving  a  spark 
from  it,  the  balls  will  diverge,  as  shown  in  Fig.  302,  thereby  man- 
ifesting the  presence  of  uncombined  electricity  at  each  end,  and 


378  NATURAL  PHILOSOPHY. 

of  a  neutral  line  near  the  center.  By  means  of  the  gold  leaf  electro- 
scope, we  may  ascertain  that  the  nearer  end,  A,  of  the  conductor 
contains  electricity  opposite  to  that  of  the  electrified  luuly,  C,  and  the 
further  end  the  same  kind.  If  0  be  positively  charged,  its  effect 
will  be  to  attract  negative  electricity  at  the  nearer  end,  A,  and  to 
repel  positive  electricity  toward  the  further  end,  B. 

There  is  no  transfer  of  any  electrical  force  in  induction, 
because  the  action  is  only  temporary ;  for  if  C  be  removed 
or  be  discharged  by  touching  it  with  the  hand,  the  balls 
immediately  collapse. 

670.  The  two  electrical   forces  may  be   separated  by 
induction.     Suppose  three  conductors  like  A  B,  placed  end 
to  end;  or,  what  is  the  same  thing,  suppose  the  conductor 
A  B  to  be  made  of  three  parts,  each  insulated  and  movable, 
and  while  the  whole  is  under  the  influence  of  a  positively 
electrified  body,  let  the  parts  be  separated  by  removing  the 
central  portion.      (1.)  This  part  will  yield  either  no  spark, 
or  a  very  feeble  positive  one.     (2.)  The  portion  B  may  be 
discharged  by  bringing  the  hand   near  it,  yielding  a  spark 
of  positive  electricity.     Its  electricity  is,  therefore,  free  to 
diffuse  itself. 

(3.)  So  long  as  A  and  C  remain  near  each  other,  neither 
can  be  discharged  by  touching  them  separately,  because 
their  electricities  are  retained  by  their  mutual  attractions. 
Electrical  forces  in  this  condition  are  said  to  be  bound. 
or  disguised.  If  communication  be  made  between  them, 
they  will  both  be  discharged  by  the  union  of  their  opposite 
forces;  or  if  the  two  are  separated,  A  will  yield  negative, 
and  C  positive  electricity. 

671.  If  the  cylinder,  A  B,  while   near  the  positive  ball, 
C,    be   touched    with    the    hand,    the   pith   balls   at  A    will 
divert-    further — th«»e    at    B    will    collapse.      As    the    hand 
and    body    are   conductor.-,    the    positive   electricity  will    be 
repelled  to  the  earth,  and  the  neutral  line  will    recede  to  an 
indefinite  di.-taiicc  from    A.      The    negative    can    not    escape, 
being  bound  by  the  attraction  of  the  positive  ball.     Oil  the 


THE  ELECTROPHOROUS. 


379 


contrary,  it  will  increase,  because  the  inductive  force  of  C 
is  no  longer  subject  to  the  counter-action  of  the  similar 
force  accumulated  in  the  end,  B.  If  the  hand  be  first  re- 
moved and  then  the  inducing  body,  the  cylinder  will  remain 
negatively  charged,  and  will  yield  all  the  phenomena  of 
free  electricity. 

Thus,  a  body  may  be  charged  by  induction  as  well  as  by  conduc- 
tion. In  conduction,  the  electrified  body  loses  a  part  of  its  force  to 
impart  the  .same  kind  of  electricity  to  an  insulated  body.  In  induc- 
tion, the  charging  body  loses  none  of  its  force,  but  excites  the  oppo- 
site kind  of  electricity  in  an  insulated  body,  which  requires  to  be 
uninsulated  for  a  time  in  the  presence  of  an  excited  body. 

672.  The  electrophorous  illustrates  the  action  of  induc- 
tion, and  affords  a  ready  supply  of  statical  electricity.     It 
consists  (1.)  of  a  cake  of  res- 
inous matter,  R,  resting  on  a 
conducting   plate   of  tin,    and 
(2.)  a  movable  metal  cover,  T, 
provided    with    an    insulating 
handle,  G. 

If  the  resinous  cake  be 
beaten  with  cat's  fur,  or  rubbed 
with  a  warm  flannel  cloth,  it 
becomes  charged  with  negative 
electricity.  If,  now,  the  cover 
be  placed  on  the  cake,  its  con- 
dition is  that  of  a  conductor 

under  the  influence  of  an  electrified  body.  Its  lower 
surface  becomes  positive  and  its  upper  negative,  by  induc- 
tion. 

If  the  cover  be  uninsulated  for  a  moment,  by  touching 
it  with  the  finger,  the  negative  force  passes  to  the  ground, 
while  the  positive  is  held  bound  by  the  negative  electricity 
of  the  resin.  If,  now,  the  finger  be  first  removed,  and 
then  the  cover  be  raised  by  means  of  its  insulating  handle, 
its  positive  electricity  diffuses  itself  over  the  cover,  and 
muy  be  made  to  yield  a  brilliant  spark  by  bringing  it  near 


FIG.  303. 


380  NATURAL   PHILOSOPHY. 

a  conductor.  The  reason  why  the  cake  does  not  discharge 
itself  into  the  cover,  is  due  (1.)  to  the  non-conducting  power 
of  the  resin,  and  (2.)  to  the  minute  inequalities  of  its  sur- 
face, which  do  not  permit  an  intimate  contact  of  the  cover. 

As  the  cake  acts  only  by  induction,  when  once  charged  it  retains 
its  electricity  for  a  long  time,  and  may  be  made  to  induce  any  num- 
ber of  successive  charges  in  the  disk.  Instead  of  the  resinous  cake  a 
sheet  of  gutta-percha,  or  a  tin  plate  coated  with  melted  sealing  wax. 
may  be  used.  The  disk  may  be  made  of  a  tin  plate,  with  a  stick  of 
scaling  wax  to  serve  for  a  handle.  This  simple  contrivance  may  be 
made  to  yield  very  excellent  results.  It  may  be  used  to  charge  mov- 
able conductors  of  a  spherical  or  cylindrical  form,  like  those  shown 
in  Fig.  302,  or  for  performing  experiments  in  which  a  continuous 
supply  of  electricity  is  not  required. 

673.  Faraday's  theory  of  induction  .supposes  (1.)  that 
all  particles  of  matter  are  more  or  less  conductors;  (2.) 
that  under  the  influence  of  an  electrified  body,  the  mole- 
cules of  the  surrounding  medium  become  arranged  in  a 

polarized  form.  Thus,  if 

c      a     6     c     d  C    represent    a    positively 

e_ ^1*       charged   body,    the   polari- 
rm  (•*(*(*  ^- ^K9     zation    of    the    contiguous 

Flo  .jQj  molecules   of  air,    and    of 

A  B,    a    distant    insulated 

conductor,  may  be  represented  by  a  series  of  black  :md 
white  hemispheres.  (3.)  That  contiguous  particles  can 
communicate  their  polarity,  more  or  less  readily,  one  to 
the  other.  Those  that  communicate  their  electrical  forces 
readily,  are  conductors;  those  that  retain  their  polarity,  or 
communicate  their  electrical  forces  with  extreme  difficulty, 
are  insulators.  (4.)  Induction  is  the  action  of  an  electri- 
fied  body  upon  insulating  matter.  If  the  insulated  cylinder, 
A  B,  be  contiguous  t<>  the  polari/ed  molecules  of  air,  its 
particles  will  also  be  polari/ed;  but,  as  they  are  conductors, 
they  will  discharge  their  electric  forces  one  into  the  other, 
ami  thereby  the  cylinder  it-elf  will  become  polarized,  as  if 
it  were  a  huge  molecule. 


INDUCTION.  381 

674.  Induction  is  essential  in  most,  if  not  all,  electrical 
phenomena. 

1.  In  utt  met  ion.     The  pith  ball  of  the  electrical  pendulum 
is   first  polarized,  like  the  cylinder,  A  B,   Fig.   304.     The 
side  next  the  excited  glass  rod  becomes  negative  by  induc- 
tion, and  as  soon  as  the  attraction  of  the  opposite  electrical 
forces  becomes  greater  than  the  repulsion   of  the  positive 
electricity  on   the  further  side  of  the  ball,  the  ball  flies  to 
the  rod. 

2.  In  charging.     In  Figs.  302  and  304,  suppose  C,  posi- 
tively charged,  to  be  brought  toward  A  B.    The  polarization 
<  >f   .V  B   will  rise  higher   and   higher,   in  proportion  as   C 
conies  nearer.     When  C  is  near  enough,  AB  will  become 
permanently   charged   with    positive    electricity,    either    by 
spark  or  by  contact.     The  most  probable  explanation  of 
this   is,  that   at   a  high  state  of  polarization   the   adjoining 
particles  discharge   their  electrical   forces  into  one  another. 
At  spark  or  at  contact  an  equal  amount  of  both  electricities 
becomes  neutralized,  and  the  cylinder  becomes  charged,  not 
by  receiving  more   positive   electricity,  but  by  discharging 
its  negative.     As  soon  as  the  negative  disappears,  the  posi- 
tive  diffuses   itself   over   the   conductor,    and    is  prevented 
from  escape  by  the   insulation   of  its  support  and  of  the 
air. 

3.  Discharging.     If,   now,  the  hand  be  brought  near  the 
positively  charged  conductor,  the  electricity  of  the  hand  is 
polarized.     Its   positive    electricity   passes    to    the    ground, 
and    its   negative  to   the   fingers.     At  contact,  the  negative 
of  the  hand  and  the  positive  of  the  cylinder  combine,  and  the 
molecules  of  the  conductor  become  unpolarized,  or  neutral. 
Hence,  we  may  say  that  the  cylinder  was  charged  by  losing 
its  negative  electricity,  and  discharged  by  losing  its  positive. 
These   terms   express  what   is  true   in  effect  though  not  in 
process. 

675.  Nothing  passes  from  particle  to  particle  but  the 


382  NATURAL  PHILOSOPHY. 

inductive  force.  This  first  develops  the  two  electrical 
forces  in  each  molecule  by  polarization,  and  then,  when  of 
sufficient  intensity,  causes  this  polarity  to  disappear  by  dis- 
charge into  contiguous  molecules.  The  molecules  of  con- 
ductors are  easily  polarized  and  discharged;  the  molecules 
of  insulators  require  a  greater  force  to  effect  polarization 
and  discharge. 

Herein  consists  the  analogy  between  magnetic  and  electrical  induc- 
tion. The  induction  of  magnetism  in  soft  iron  is  instantaneous  but 
temporary;  that  of  steel  is  effected  with  greater  difficulty,  but  is  per- 
manent. The  analogy  is  not  complete  in  other  respects,  especially  in 
this,  that  in  magnetic  induction  the  two  forces  can  not  be  separated. 
Nevertheless,  the  polar  character  of  electricity  is  sustained  even  in 
electrical  induction,  for,  although  a  body  may  be  charged  positively 
or  negatively,  yet  this  can  only  be  effected  and  maintained  by  the 
opposite  force  induced  in  the  insulating  molecules  which  surround  it. 

676.  Electricity  is  found  only  on  the  surface  of  an  insu- 
lated conductor.  This  is  a  direct  consequence  of  the  pre- 
ceding, and  may  easily  be  verified.  Let  a  brass  ball  be 
suspended  by  a  silk  thread,  and  be  covered  with  two  closely 


Fio.  305. 


fitting  hemispheres  of  brass,  provided  with  insulating  han- 
dles. If  a  charge  be  communicated  to  the  apparatus  so 
compounded,  and  tin-  hemispheres  be  withdrawn,  no  elec- 
tricity whatever  will  remain  on  the  sphere.  Hence,  a 
hollow  conductor  i-  as  -.-rvicrable  ;i>  \\  solid  one. 


ELECTRICAL   APPARATUS.  383 

677.  The  charge  is   distributed   uniformly  only  in   the 
case  of  the   sphere.     If  the   conductor  be  a   cylinder  with 
rounded  ends,  the  intensity  will  be  least  at  the  center  and 
greatest  at  the  ends,  as  represented  by  the  divergence  of 
the  balls  in   Fig.   302.     The  more  pointed  the  ends,  the 
greater  will  be  the  accumulation  of  intensity  at  the  extrem- 
itics.     The  effect  of  a  point,  either  on   a  charged  surface, 
or  turned  toward  a  charged  surface,  is  such  as  to  discharge 
a  body   with  extreme  facility,   and   generally  without  the 
passage  of  a  spark. 

678.  The  terms  quantity  and  intensity  will  be  under- 
stood by  reference  to  the  analogous  use  of  the  terms  with 
respect  to  heat;  thus,  the  heat  of  molten  iron  is  intense, 
but  a  hogshead  of  boiling  water  contains  a  greater  quantity 
of  heat    than   a   pound  of  molten  iron.     In  one  case,  each 
particle  is  in  very  rapid  vibration,  in  the  other  very  many 
particles  are  in  vibration,  and  the  sum  of  all  the  vibrations 
determines  the  quantity.     Electrical  intensity  has   reference 
to  the  amount  of  force  lodged  in  each  particle ;  quantity  of 
electricity  has   reference   both   to   the   number  of  particles 
affected   and   to  the  force   lodged   in  each.     Of  course,  in 
every  electrified  body,  there  is  both  quantity  and  intensity, 
but  the  charge  may  be  characterized  by  the  predominance  of 
either  quality.     In  statical  electricity,  the  quantity  is  always 
small,  though  its  intensity  is  sometimes  enormous.    The  in- 
tensity is  due  to  a  high  state  of  polarization,  and  is  measured 
by   its  power  to  effect  discharge   through   bad    conductors. 
Thus,  a  long  spark  is  an  evidence  of  great  intensity. 

ELECTRICAL    APPARATUS. 

679.  An  electrical  machine  is  an  apparatus  by  means  of 
which  large  supplies  of  statical  electricity  may  be  developed 
in  a  convenient  manner. 

Fig.  306  represents  Winter's   plate  machine,  which    is  one  of  the 
best.     This  consists  of  a  circular  plate  of  glass,  mounted  on  a  glass 


384 


NATURAL   PHILOSOPHY. 


axis,  which  is  supported  by  two  posts  of  glass  or  of  dry  wood,  and 
made  to  revolve  by  a  winch. 

Friction  is  applied  to 
the  glass  by  means  of 
two  rubbers,  R,  made  of 
stuffed  leather,  and  coated 
witli  an  amalgam  of  mer- 
cury, tin,  and  zinc.  The 
rubbers  are  kept  in  place 
by  means  of  a  pair  of 
clamps  attached  to  an 
insulated  brass  hall,  N, 
called  the  negative  con- 
ductor. Attached  to  the 
rubber  are  two  wings  of 
silk,  to  prevent  the  elec- 
tricity from  escaping  into 
the  air. 

The  plate  also  passes 
between  two  wooden 
rings,  W,  which  are  at- 
tached to  an  insulated 
brass  ball,  P,  known  as 
the  prime  conductor.  On 

the  side  of  the  wooden  rings,  next  the  glass  plate,  are  two  rows  of 
brass  points,  which  are  connected  by  means  of  tin  foil  to  the  prime 
conductor. 

On  turning  the  plate,  negative  electricity  is  developed  on 
the  rubbers  and  conducted  to  the  negative  conductor,  N,  and 
positive  electricity  is  developed  on  the  glass  plate.  As  the 
plate  revolves,  the  positive  electricity  of  the  glass  acts  by 
induction  on  the  prime  conductor,  attracting  its  negative 
electricity.  This  negative  electricity  collects  on  the  points 
inside  of  the  rings,  W,  and  finally  attains  sufficient  inten- 
-ity  t->  pass  through  the  intervening  space  of  air  and  unite 
with  the  positive  electricity  on  the  glass,  and  thcrchv  render 
ttl  -urf'acc  neutral.  The  prime  conductor,  then-Ion-,  Drives 
up  its  negative  and  remain-;  eh:irged  with  positive  electricity, 
in  the  manner  described  in  (674). 

680.  If  both  the  conductors  were  insulated,  this  action 


FIG.  30f>. 


WINTER'S  MACHINE.  385 

would  speedily  cease,  because  the  positive  electricity  of  the 
prime  conductor  would  act  inductively  on  the  negative  of 
the  other  conductor,  and  thus  only  a  feeble  charge  would 
be  possible.  If  either  conductor  be  uninsulated,  its  tension 
will  he  reduced  to  zero,  and  thereby  leave  the  electric  force 
on  the  other  conductor  free.  Hence,  when  the  rubbers  are 
connected  to  the  ground  by  means  of  a  chain,  positive  elec- 
tricity is  accumulated  on  the  prime  conductor. 

When  negative  electricity  is  wanted,  the  chain  is  removed 
from  the  rubbers  and  attached  to  the  prime  conductor,  and 
the  negative  electricity  accumulates  on  the  negative  con- 
ductor. If  the  hand  is  brought  near  either  conductor  when 
charged,  a  spark  follows,  which  is  renewed  as  the  plate  is 
turned. 

The  length  of  the  spark  is  wonderfully  increased  by  the 
addition  of  a  large  wooden  ring,  I,  surmounting  the  prime 
conductor.  An  iron  wire  forms  the  core  of  this  ring,  and 
is  in  metallic  connection  with  the  prime  conductor.  The 
wooden  ring  acts  inductively  on  the  prime  conductor  and 
prevents  discharge  until  the  electric  force  attains  a  high 
tension.  Without  the  ring,  which  may  be  removed  at  the 
pleasure  of  the  operator,  the  machine  will  give  a  rapid  suc- 
cession of  sparks,  two  inches  in  length  ;  with  the  ring,  sparks 
may  be  obtained  six  or  seven  times  as  long,  but  these  are 
proportionally  less  frequent.  The  quantity  of  electricity 
developed  is  the  same  in  both  cases. 

There  are  many  other  electrical  machines  having  the  same  action 
as  the  one  described.  Among  these  are  several  varieties  of  the  plate 
machine,  and  others  in  which  a  hollow  cylinder  of  glass  is  substituted 
for  the  glass  plate.  Electricity  may  also  be  generated  in  enormous 
quantity  by  the  friction  of  steam  passing  through  jet  pipes  of  hard 
wood.  A  hydro-electric  machine,  constructed  on  this  principle,  yielded 
sparks  twenty-two  inches  long,  and  was  capable  of  fully  charging  a 
battery  of  thirty-six  large  Leyden  jars  upward  of  sixty  times  a 
minute. 

ir<-  681.  There  are  other  machines  which  act  on  the  principle 
of  the  electrophorous.     In  Holtz's  machine,  Fig.  307,  elec^ 

N.  P.  25. 


386 


NA  T  URA  L     PHIL  OS  OP  11  \ '. 


tricity  is  developed  by  the  continuous  inductive  action  of  a 
body  already  electrified. 

It  consists  of  two  circular  plates  of  glass,  about  one-tenth  of  an  inch 
apart.  The  larger  one,  A,  is  fixed  and  insulated ;  the  smaller,  B,  turns 
on  a  glass  axis,  which  passes  through  a  hole  in  the  center  of  the  fixed 
plate.  In  the  plate,  A,  are  two  openings,  each  furnished  with  an  ar- 
mature. These  armatures  consist  of  a  band  of  paper  terminating  in 
a  sort  of  tongue,  which  is  glued  to  the  glass  so  that  the  tongues,  //', 
project  into  the  window. 


Fm.  307. 


In  front  of  the  armatures,  but  on  the  other  side  of  the  movable 
plat.-,  B,  are  two  brass  combs,  P  P',  supported  by  two  brass  rods. 
Through  the  rounded  ends  of  these  rods  arc  inserted  two  smaller 
rods,  terminating  in  knobs,  ///  and  //,  which  are  called  the  /W<w  of  the 
machine.  These  poles  may  be  inclined  to  each  other  or  placed  at  any 
distance  apart  by  means  of  a  wooden  handle  attached  i<,  ,//.  Finally, 
a  very  rapid  rotation  may  b»-  Driven  to  the  plate.  I),  by  means  of  the 
multiplying  wheels  shown  on  the  right  of  tin-  figure. 


HOLTZ'S  MACHINE.  387 

682.  To  obtain  electricity,  the  poles  are  brought  in  contact 
and  one  of  the  armatures  slightly  charged.     For  instance, 
let  /  be  charged  negatively  by  touching  it  with  an  excited 
rod  of  ebonite.     The  armature  will  then  act  inductively  on 
the  plate,  repelling  negative  electricity  to  the  comb  P,  and 
leaving  the  nearer  surface  of  the  glass  positively  charged. 
On  turning  the  maphine,  these  positively  charged  particles 
will  be  brought  in  front  of  the  armature  /',  and  a  second 
induction  takes  place,  viz. :  the  positive  glass  attracts  nega- 
tive electricity  to  itself,  and  sets  free  positive  electricity  on 
the  armature  /'. 

After  a  few  turns  the  armatures  will  become  charged  with 
opposite  electricities,  and  the  poles  may  be  gradually  sepa- 
rated, as  shown  in  the  figure.  There  will  occur  immedi- 
ately a  succession  of  sparks,  which  results  from  the  reunion 
of  the  electricities  of  the  two  poles.  Under  the  conditions 
indicated,  n  will  be  the  negative  and  m  the  positive  pole. 
The  power  of  the  machine  increases  rapidly  for  a  short 
time,  and  then  becomes  constant. 

Though  this  machine  under  favorable  circumstances  is  far  more 
powerful  than  the  plate  machine,  it  is  less  reliable,  for  it  requires 
nearly  perfect  insulation,  and  is  more  seriously  affected  by  the  hu- 
midity of  the  air.  Instead  of  the  fixed  plate,  A,  any  number  of  insu- 
lated sectors  of  glass,  provided  with  paper  armatures,  may  be  em- 
ployed. By  connecting  one  of  the  poles  with  the  ground,  the  other 
may  be  used  as  a  prime  conductor.  "/flN 

683.  There  is  a  limit  to  the  accumulation  of  the  electric 
force  on  any  surface.     But  if  two  conducting  surfaces  are 
separated  by  an  insulating  medium  capable  of  being  highly 
polarized,  the  intensity  will  be  increased  by  reason  of  the 
reciprocal  inducing  action  of  the  two  surfaces.    Any  arrange- 
ment of  this  sort  is  said  to  act  as  a  condenser. 

684.  The  Leyden  jar  is  the  most  convenient  form  of  the 
condenser.     This   consists  of  a  glass  bottle  coated  both  on 
the  inner  and  the  outer  surface  with  tin  foil  to  within  three 
inches  of  the  neck.     The  mouth  is   usually  closed  with  a 


388  NATURAL   PHILOSOPHY. 

plug  of  varnished  wood,  through  which  passes  a  brass  wire 
surmounted  by  a  knob,  and  connected  to  the  inner  coating 
by  means  of  a  chain.  If  the  jar  be  held  near  a  machine  in 
action,  as  shown  in  Fig.  308,  the  sparks  will  pass  from  the 

machine  to  the  interior 
of  the  jar ;  but  after  a 
little  while  this  will 
cease,  and  the  jar  is 
then  said  to  be  charged. 
To  discharge  the  jar, 
the  inner  and  outer 
coatings  must  be 
brought  in  connection. 

FIG.  308.  This  may  be  done  by 

placing    one    hand    on 

the  outer  coating,  and  bringing  the  other  hand  near  the 
knob.  A  brilliant  spark  will  then  pass  from  the  knob,  and 
the  experimenter  receives  a  peculiar  twitching  sensation, 
called  the  electric  shock.  As  this  shock  is  inconvenient  and 
sometimes  dangerous,  the  discharge  is  usually  effected  by 
means  of  a  discharging  rod,  which  consists  of  a  jointed  wire 
terminating  in  brass  knobs.  See  Fig.  321. 

If  the  outer  coating  be  insulated,  the  jar  will  receive 
little  or  no  charge.  But  if  the  finger  be  then  brought  near 
the  outer  coating,  for  every  spark  that  passes  into  the  jar, 
an  equal  spark  of  the  same  kind  will  pass  from  the  outer 
coating  to  the  finger.  Hence,  a  jar  contains  no  more  of 
either  electric  force  when  charged  than  before. 

Several  Leyden  jars,  standing  side  by  side,  and  having  their  simi- 
lar coatings  connected,  the  outer  by  means  of  tin  foil  ami  the  inner 
by  wires,  constitute  an  electrical  battery.  Such  an  arrangement  is 
shown  in  Fig.  321. 

685.  The  action  of  the  jar  may  be  thus  explained:  when 
a  positive  spark  passes  to  the  interior  of  the  jar,  the  mole- 
cules of  the  glass  are  all  polarized,  as  shown  in  Ki.ir.  309. 
If  the  jar  be  insulated,  but  little  charge  can  be  received,  be- 


THEORY   OF   THE  LEY  DEN  JAR. 


389 


4.  ,- 

_^  __  '  V_ 


FIG.  309. 


FIG.  310. 


cause  of  the  repulsion  of  positive  electricity,  which  accumu- 
lates on  the  outer  coat- 
ing.   If,  now,  the  outer      i  o         i  o 
coating    be     connected 
with    the    ground,    the 
positive    electricity   es- 
capes from  it,  and,  con- 
sequently,    this     layer 
becomes    charged    with 
negative  electricity,  as  represented  in  Fig.  310. 

The  outer  surface  is,  therefore,  charged  by  induction,  and 
the  negative  electricity  will  not  escape  from  it,  because  it  is. 
bound  by  the  attraction  of  the  positive  on  the  inner  surface. 
The  amount  of  charge  which  a  jar  may  receive  is  in  propor- 
tion to  the  facility  it  has  for  induction.  The  thinner  the 
glass  the  better;  but  if  too  thin,  the  polarization  may  rise 
high  enough  to  cause  a  discharge  sufficient  to  break  the  glass. 

The  charge  is,  therefore,  dependent  rather  on  the  glass 
than  on  the  coatings.  This  is  shown  by  means  of  a  jar  with 
movable  tin  coatings,  Fig.  311.  If  the 
parts  be  put  together  and  the  jar  charged, 
the  coatings  may  be  removed  and  dis- 
charged: now,  on  replacing  the  parts,  a 
charge  may  be  received  from  the  jar 
almost  as  strong  as  if  the  coatings  had 
not  been  removed.  So,  also,  the  glass 
cup,  B,  may  be  charged  separately  by 
rotating  its  inner  surface  on  a  knob  con- 
nected with  the  prime  conductor,  and  then, 
after  the  two  coatings  are  applied,  the  whole 
combination  may  be  discharged  by  a  single 
spark.  Hence,  the  principal  office  of  the 
coatings  is  that  of  a  conductor  to  connect 
the  polarized  molecules  of  the  glass. 


686.  If  a   series  of  jars  be  insulated 
except  the  last,   as   represented   in   Fig. 


FIG.  311. 


390 


NATURAL  PHILOSOPHY. 


312,  all  may  be  charged  simultaneously.  The  electricity 
repelled  from  the  first,  charges  the  second,  and  so  on.  This 
is  called  the  charge  by  cascade.  Each  may  be  discharged 
singly,  or  they  may  be  connected  to  form  an  electrical 
battery. 


FIG.  312. 


687.  A  small  quantity  of  free  electricity  is  usually  found 
in  a  charged  jar,  which  is  due  to  the  polarization  of  the  air 
and  other  bodies  surrounding  the  jar.  If  the  jar  be  insu- 
lated, and  the  finger  be 
brought  near  the  knob, 
the  free  charge  will  pass 
to  the  finger.  An  equal 
spark  may  now  be  ob- 
tained from  the  outer 
coating.  By  touching 
alternately  the  inner  and 
outer  coating,  an  insu- 
lated jar  may  be  gradu- 
ally discharged. 

Tliis  is  prettily  shown  hy 
the    apparatus    in    Vlg.    :J1.'I. 
Between  the  two  hells,  con- 
Fio.  313.  nected    with    the    innrr    and 

outer  coatings  of  the  jar,  is 

<u-|. ended  a  litrht  <-.,pjn.r  hall,  hy  means  of  silk  thread.  The  hall  is 
attracted  first  hy  one  hell  and  then  the  other,  and  so  on  lor  a  con- 
siderable time,  receiving  at  each  contact  the  free  electricity  of  the 
bell,  until  the  jar  is 


ELECTRICAL   EXPERIMENTS. 


391 


ELECTRICAL    PHENOMENA. 

688.  By  means  of  the  electrical  machine  and  the  Leyden 
jar,  a  great  number  of  striking  experiments  may  be  per- 
formed, which  illustrate  the  laws  and  exhibit  the  effects  of 
electricity. 

1.  Repulsion.     If  a  doll's  head,  with  hair  affixed  to  it,  be 
placed   on   the   prime   conductor  when    the    machine   is    in 
action,  the  hairs  will  stand  out  apart  from  each  other,  be- 
cause they  are  charged  with  the  same  electrical  force. 

This  experiment  may  be  repeated  by  placing  a  person  on  an  insu- 
lating stool.  This  is  merely  a  low  stool  with  glass  legs.  When  the 
person  touches  the  prime  conductor  he  becomes,  in  fact,  a  part  of  it, 
and  sparks  may  be  drawn  from  him  with  the  same  effect  as  from  the 
cylinder. 

2.  Attraction.     If  a  bystander  place  his   hand   near  the 
hairs  excited  in  the  previous  experiment,  they  will  converge 
toward  it.     Negative  electricity  is  induced  in  his  hand,  and 
the  two  bodies  oppositely  electrified  attract  each  other. 

3.  Attraction  and   repulsion.       The    electrical    chimes,    Fig. 
314,   consists   of   two   bells  in   metallic 

connection  with  the  machine,  and  of  a 
third  bell  insulated  by  a  silk  thread 
from  the  machine,  but  in  communica- 
tion with  the  ground.  Between  the  bells 
are  small  brass  balls  suspended  by  silk 
threads.  On  working  the  machine,  the 
outer  bells  become  positively  electri- 
fied, and  induce  negative  electricity  in 
the  middle  bell.  The  balls  are,  there- 
fore, alternately  attracted  and  repelled 
by  the  outer  and  inner  bells,  and  thus 
a  constant  ringing  is  kept  up.  FIG.  SH. 

The  electrical  hail  is  exhibited  by  means  of  two  metal 
plates,  one  connected  with  the  machine,  and  the  other  with 
the  ground,  as  in  Fig.  315.  If  light  pith  balls  be  placed 


392 


NATURAL   PHILOSOPHY. 


between  the  plates  and  the  machine  set  in  action,  the  balls 
will  rise  and  fall  in  an  irregular  shower. 

A  variation  of  this  experiment  consists  in 
placing  grotesque  figures  of  pith  or  paper  be- 
tween the  plates. 

689.  The  kinds  of  discharge  are  three: 
(1.)  conductive,  (2.)  convective,  (3.)  dis- 
ruptive. 

The  conductive  discharge  is  effected 
without  light,  when  the  electricity  passes 
through  a  good  conductor. 

The  convective  discharge  is  usually  ef- 
fected by  the  movement  of  particles  of 
air  passing  away  from  a  point  on  a 
charged  surface.  Solid  particles  may 
also  be  the  medium  of  convective  dis- 
charge, as  in  the  case  of  the  electrical 
hail.  In  such  cases  the  electricity  is 
carried  away  from  the  electrified  body 
by  means  of  these  charged  particles. 

Quite  a  current  of  air  may  be  detected  by  persons  stand- 
ing near  the  point.  The  face  feels 
as  if  a  cobweb  were  drawn  over  it. 
The  electric  whirl  consists  of  a  num- 
ber of  such  points  suspended  on  a 
pivot.  Fig.  316.  The  reaction  of 
the  current  upon  the  air  is  suffi- 
cient to  move  the  wheel  rapidly 
about. 

Flames  act  as  points.  If  a  candle 
be  held  near  the  charged  conductor, 
the  flame  will  be  repelled,  a.-  shown 
in  Fig.  317.  If  th(M-an«H«-  In-  placed 
on  tho  machine  ami  a  point  he  turned 
toward  it,  the  flame  will  he  driven  in  a  contrary  direction. 


FIG.  315. 


LUMINOUS  EFFECTS. 


393 


This  is  due  to  the  current  of  air  which  sets  out  from 
the  point,  which  has  become  negatively  electrified  by  in- 
duction. 

3.  The  disruptive  charge 
is  effected  through  a  bad 
conductor,  and  is  attended 
by  the  evolution  of  light. 

This  light  is  not  electricity, 
but  is  due  to  the  molecular 
disturbance  of  the  particles 
through  which  the  electric 
force  passes.  This  is  proved 
(1.)  by  the  actual  transfer  of 

solid  particles  from  one  con-  FlG  317 

ductor    to    another,  and    (2.) 

by  the  fact  that  the  color  of  the  light  varies  with  the  medium  through 
which  it  passes. 

There  are  three  varieties  of  the  disruptive  discharge : 
(1.)  the  spark,  (2.)  the  brush,  (3.)  the  glow. 

Ttie  spark  is  the  most  energetic  form  of  the  discharge,  and 
varies  in  form  from  a  straight  line  to  a  zigzag  line,  with 
strongly  marked  lateral  branches.  The  brush  may  be  re- 
garded as  a  rapid  succession  of  feeble  sparks.  The  brush  is 
readily  obtained  wrhen  the  discharge  occurs  between  the  edge 
of  a  metallic  plate  and  a  poor  conductor.  It  has  the  form 
of  a  bush  without  leaves,  and  is  accompanied  by  a  low, 
hissing  sound.  When  a  feeble  charge  escapes  from  a  point, 
the  light  is  simply  a  quiet  glow.  This  is  best  exhibited  in 
the  dark. 

690.  Luminous  effects.  If  a  discharge  be  passed  through 
an  interrupted  conductor,  a  succession  of  sparks  will  be 
obtained,  which,  when  exhibited  in  a  darkened  room,  yield 
a  brilliant  display.  The  luminous  tube,  Fig.  318,  may  be 
used  for  this  purpose.  It  consists  of  a  glass  tube  on  which 
are  pasted,  in  a  spiral  form,  bits  of  tin  foil.  The  luminous 
pane  is  constructed  on  the  same  principle  on  a  pane  of 
glass. 


394 


NATURAL   PHILOSOPHY. 


If  the  discharge  is  effected   in  rarefied  gases,  the  effect 
is  very  beautiful.     For  this  purpose  a  receiver,  called  the 
Aurora  tube,  Fig.  319,   is 
used.     In  rarefied  air,  the 
light  is   intense  and  of  a 
bluish  color ;  in  nitrogen, 
the  sparks  are  more  of  a 
purple  ;  in  hydrogen,  of  a 
fine  crimson  color. 


691.  Duration  of  the 
spark.  If  Newton's  wheel, 
Fig.  221,  be  set  in  very 
rapid  revolution  in  a  dark- 
ened room,  and  be  illumi- 
nated by  an  electric 
spark,  the  wheel  will  ap- 
pear stationary.  This 
shows  that  the  spark  must 
be  of  very  brief  duration, 
inasmuch  as  it  fails  to 
illuminate  the  wheel  in 
FIG.  sis.  two  successive  positions.  FIQ.  319. 

By  applying   this   princi- 
ple, it  has  been  shown  that  the  duration  of  the  spark  is  less 
than  one  millionth  part  of  a  second. 

692.  The  velocity  of  the  discharge  has  been  measured 
by  transmitting  the  discharge  of  a  Leyden  jar  through  a 
very  long  copper  wire.  The  circuit  was  broken  at  three 
points;  one  at  the  middle  of  the  wire,  and  one  near  each 
coating  of  the  jar.  In  this  way  three  sparks  were  formed, 
which  to  the  eye  appeared  simultaneous  ;  hut  when  they 
were  viewed  by  means  of  a  revolving  mirror, 
they  presented  the  appearance  of  three  arcs  of 
equal  length,  \\ith  the  middle  one  rather  behind 
the  others  Fig.  320. 
By  knowing  the  velocity  with  which  the  mirror  revolved, 


CALORIFIC  EFFECTS. 


395 


the  amount  of  retardation  was  found,  and  the  velocity  of  the 
electric  discharge  in  copper  was  estimated  to  be  two  hundred 
and  eighty-eight  thousand  miles  per  second.  The  velocity 
varies  with  the  intensity  of  the  charge,  and  also  with  the 
nature  of  the  medium. 

693.  Calorific  effects.  It  has  already  been  mentioned 
that  coal  gas  may  be  ignited  by  a  spark.  Any  combustible 
substance,  as  ether,  alcohol,  or  phosphorus,  is  readily  in- 
flamed by  a  discharge  from  a  single  Leyden  jar.  Very  thin 
wires  may  be  melted  by  a  discharge  from  a  battery.  It  is 
noticeable,  that  those  wires  are  heated  most  which  are  the 
worst  conductors.  Fig.  321  shows  the  arrangement  em- 
ployed to  communicate  an  intense  discharge.  B  is  a  battery 
of  nine  jars,  J  a  discharging  rod,  furnished  with  two  glass 
handles  for  safety,  and  U  is  called  an  universal  discharger. 


FIG.  321. 

This  consists  of  three  glass  posts,  two  of  which  carry 
jointed  rods,  while  the  center  bears  on  its  top  a  glass  plate. 
A  thin  gold  wire,  a  b,  supported  on  this  plate  by  a  paper 
card,  c,  is  instantly  volatilized  by  a  powerful  discharge. 

694.  Chemical  effects.  Electricity  is  an  efficient  agent 
in  producing  chemical  changes.  The  peculiar  odor  which 
accompanies  the  electrical  discharge,  has  been  traced  to  the 


396  NATURAL   PHILOSOPHY. 

formation  of  ozone,  which  is  an  active  allotropic  state  of 
oxygen.  If  a  succession  of  sparks  be  passed  through  •  am- 
monia, or  through  carbonic  acid  gas,  it  will  be  decomposed. 
The  spark  may  also  effect  combination. 

Thus,  if  two  volumes  of  hydrogen  and  one  of 
oxygen  be  mixed  in  the  electrical  pistol,  Fig.  322, 
a  single  spark  will  cause  them  to  combine  with 
a  loud  explosion.  To  this  same  cause  is  attrib- 
uted the  presence  of  nitric  acid  in  the  air  during 
a  thunder-storm. 

695.  The   magnetic    effects    of  statical 
electricity  are  not  as   marked  as  those  of 
dynamical     electricity.       Nevertheless,     a 
i.  322.  steel  wire  may  be  magnetized  by  the  dis- 

charge of  a  large  Leyden  jar. 

696.  The  mechanical  effects  are  shown  when  a  discharge 
passes  through  a  poor  conductor.     If  a  thick  paper  card  be 
placed  between  the  rods  of  the  universal  discharger,  a  mod- 
erate  charge  will  perforate   the  card,  producing  a  burr  in 
both  directions.     A  stronger  charge  will   perforate  a  glass 
plate  similarly  placed. 

The  mechanical  effects  of  lightning  are  well  known.  It  rends  and 
tears  every  obstacle,  which  hinders  its  free  transmission,  with  amazing 
force.  The  noise  which  accompanies  the  spark  is  due  to  the  sudden 
expansion  of  the  surrounding  air,  followed  by  a  sudden  collapse, 
thereby  producing  a  sonorous  wave  of  condensation  and  rarefaction. 

697.  Physiological  effects.     A  moderate  discharge,  sent 
through  the  human  body,  will  produce  a  decided  shock. 

Quite  a  number  of  persons  may  receive  the  shock  simultaneously. 
For  this  purpose  all  must  join  hands,  the  first  touching  the  outside 
of  a  Leyden  jar,  and  the  last  the  knob.  The  Abbe  Nollet  com- 
municated a  shock  to  an  entire  regiment  of  thirteen  hundred  men. 
With  large  Leyden  jars  and  batteries,  the  discharge  is  dan^-riMi.-. 

Electricity  has  also  been  found  of  service  in  the  treatment  of  some 
diseases.  For  this  purpose,  as  well  as  for  producing  ehemii-al  decom- 
position and  magnetic  effects,  some  form  of  dynamical  electricity  is 
generally  employed. 


ATMOSPHERIC  ELECTRICITY.  397 

ATMOSPHERIC    ELECTRICITY. 

698.  Franklin   demonstrated,  in  1752,  that  a  flash  of 
lightning  is  simply  an  enormous  spark  of  electricity.     This 
he  proved  by  raising  a  silk  kite  at  the  approach  of  a  storm. 
As  soon  as  the  rain  had  wetted  his  hempen  kite  string,  and 
thereby  rendered  it  a  good  conductor,  he  succeeded  in  draw- 
ing sparks  from  a  key  attached  to  the  string,  and  in  charging 
a  Leyden  jar. 

It  is  now  known  that  the  atmosphere  is  sensibly  electrical 
in  all  weathers,  but  that  it  varies  both  in  the  kind  of  elec- 
tricity present  and  also  in  its  intensity.  It  is  more  intense 
in  summer  than  in  winter,  and,  as  a  general  rule,  a  little 
before  noon  than  in  the  afternoon  of  each  day.  The  devel- 
opment of  this  electricity  has  been  attributed  to  the  friction 
of  the  air,  to  combustion,  to  vegetation,  and  to  the  induction 
from  the  earth ;  and  although  many  of  these  causes  may 
contribute  to  the  phenomena,  it  is  now  generally  supposed 
that  the  principal  source  of  atmospheric  electricity  is  the 
evaporation  and  subsequent  condensation  of  water. 

699.  A  cloud  will  become  positively  electrified  by  the 
accumulation  of  the  electricity  which,  before  its  formation, 
was   disseminated   through   the   particles    of  air    which    it 
contains. 

The  watery  particles  of  the  cloud  being  good  conductors,  permit 
the  free  discharge  of  the  electrified  particles,  and  thereby  the  elec- 
tricity accumulates  on  the  surface  in  considerable  intensity. 

Negative  clouds  may  be  similarly  charged,  but  it  is 
probable  that  the  majority  of  them  are  due  to  the  inductive 
action  of  a  cloud  more  powerfully  charged  than  themselves. 
By  the  presence  of  such  a  cloud  their  positive  electricity 
will  be  repelled  to  other  clouds  or  to  the  earth,  and  they 
will  retain  only  negative  electricity. 

The  earth  beneath  any  cloud  is  subject  to  the  same  inductive  action, 
and  will  become,  by  consequence,  charged  with  electricity  opposite 
to  that  of  the  cloud. 


398  NATURAL   PHILOSOPHY. 

700.  Lightning.     The   air    between   a   strongly   charged 
cloud   and   an   oppositely   charged   adjacent   body   becomes 
polarized,  and  when  the  tension  passes  a  certain  limit,  the 
two  electrical  forces  unite  with  a  dazzling  flash  of  lightning. 
The  lightning  may  therefore  pass  from  cloud  to  cloud,  from 
a  cloud  to  the  earth,  or  from  the  earth  to  a  cloud. 

701.  The  thunder  is  due  to  the  violent  commotion  pro- 
duced in  the  air  by  the   passage  of  a  flash  of  lightning. 
The  rolling  peal  may  be  due  to  several  reports  produced  by 
the  same  flash,  or  to  the  multiplied  echoes  reflected  from 
the  clouds  and  the  earth,  or  to  both  causes  combined. 

702.  Heat  lightning  is  the  name  applied  to  bright  flashes 
of  light  often    observed    in    the    horizon    during    summer 
evenings.     This  is  generally  due  to   the  reflection  by  the 
atmosphere  of  ordinary  lightning  so  distant  that  the  thunder 
is  inaudible. 

703.  The  distance  of  the  lightning  may  be  computed  by 
measuring  the  interval  between  the  flash  and  the  report. 

The  passage  of  light  may  be  regarded  as  instantaneous,  while  sound 
moves  about  eleven  hundred  and  twenty  feet  per  second.  Hence,  if 
five  seconds  elapse  between  the  flash  and  the  thunder,  the  lightning 
must  have  been  more  than  a  mile  distant.  No  danger  need  be  antici- 
pated in  a  thunder-storm,  unless  the  quick  succession  of  lightning 
and  thunder  indicates  that  electric  clouds  are  near  at  hand. 

704.  The  position  of  greatest  safety  during  a  thunder- 
storm is  obtained,  if  out  of  doors,  by  taking  shelter  under 
low  sheds  and  buildings.     Tall   trees  or  houses   should  be 
avoided,  because  elevated  objects  are  most  likely  to  receive 
the  discharge.     Within  doors,  a  person   may  become  insu- 
lated and,  therefore,  tolerably  safe,  by  standing  on  a  thick 
carpet,  or  by  reclining  on  blankets  and  feather  mattresses. 
It  is  always  injudicious  to  stand  near  a  good  conductor  that 
is   not    in    free    communication    with    the   ground:    hence, 
the  chimney  should  be  avoided  because  of  the   en  ml  net  ing 
power  of  soot;    so,  also,  should   bell  wires,  gilt   molding. 


AURORA    BOREALIS.  399 

and  open  windows.     Experience  has  also  shown  that  cellars 
are  unsafe  places  for  refuge. 

705.  Lightning   conductors   are    metallic    rods    used    to 
protect  buildings  against  the  effects  of  lightning.     The  most 
available   material  is   galvanized   iron,   tipped  with   gilded 
points.     The  rod  should  be  continuous  from  top  to  bottom, 
and  should  terminate  at  the   bottom  in  earth  permanently 
moist. 

A  lightning  rod  affords  protection  in  two  ways :  (1.)  by  preventing 
the  flash.  The  nearer  an  object  is  to  an  electrified  cloud,  the  greater 
will  be  the  inductive  action  of  the  cloud  on  the  object,  and,  by  con- 
sequence, the  greater  the  polarization  of  the  air  between  them. 
Hence,  if  such  objects  are  provided  with  a  series  of  points  extending 
to  some  distance  above  them,  the  electricity  will  be  dissipated  before 
it  has  attained  sufficient  tension  to  produce  a  disruptive  discharge. 
If,  however,  the  pointed  rods  are  not  sufficient  to  prevent  this  dis- 
charge, the  rods  protect  the  building  (2.)  by  offering  to  the  discharge 
the  line  of  smallest  resistance.  The  rod  should  be  so  large  that  it 
can  not  be  melted,  and  should  be  connected  with  any  external  metallic 
surface,  as  tin  roofs  and  gutters. 

Experiment  has  shown  that  a  rod  protects  a  conical  surface  about 
it,  the  radius  of  whose  base  is  approximately  twice  the  height  of  the 
rod.  Hence,  when  the  building  is  large,  it  is  necessary  to  have  several 
points,  projecting  at  various  places  from  the  roof,  and  to  have  all  so 
connected  as  to  form  one  or  more  conducting  systems.  If  the  light- 
ning rod  is  badly  constructed,  as,  for  instance,  if  there  are  breaks  in 
it,  or  if  it  terminates  in  dry  earth,  the  danger  is  increased,  because 
there  is  then  greater  liability  to  lateral  discharge  through  the  build- 
ing. 

706.  The  Aurora  Borealis,  or  Northern  Lights,  are  lu- 
minous appearances  observed  in  the  northern  sky,  of  differ- 
ent colors  and  of  variable  brilliancy  and  forms.     Similar 
phenomena,  called  the  Aurora  Aiistrcdis,  are  witnessed  in 
the    southern    hemisphere.      Frequently    they    form    great 
arches  in   the  sky,  more  or  less   broken,  traversed  contin- 
ually by  great  waves  of  light  shooting  across  them.     The 
brightest  exhibitions  are  always  near  the  poles. 

During  the  exhibition  of  the  aurora  (1.)    the  magnetic  needle  is 


400  NATURAL   PHILOSOPHY. 

disturbed,  and  this  disturbance  has  been  found  to  increase  with  the 
brilliancy  and  extent  of  the  aurora.  (2.)  The  telegraph  lines  are  so  far 
a  fleeted  as  to  prevent  sending  intelligible  dispatches.  (3.)  Neverthe- 
less, telegraphs  were  worked  without  the  aid  of  a  battery  during  the 
auroras  of  1859.  (4.)  In  other  ways  the  phenomena  are  so  similar 
to  those  of  electricity,  that  we  are  justified  in  assuming  that  auroral 
light  is  electric  light. 

It  has  not  been  settled  whether  the  aurora  and  the  effects  described 
are  not  all  due  to  magnetic  currents,  or  whether  the  aurora  is  itself 
an  electrical  current  producing  these  effects.  Many  observations  in- 
dicate a  maximum  of  brilliancy  every  ten  years,  which  seems  to 
point  to  some  connection  between  the  auroras,  terrestrial  magnetism, 
and  solar  heat.  (658,  659.) 

707.  Recapitulation. 

I.  The  phenomena  of  statical  electricity  are : 

1.  Excitation {  By  Motion. 

I  By  other  molecular  disturbances. 

2.  Attraction  of  bodies  charged  with  unlike  electricities. 

3.  Repulsion  of  bodies  charged  with  like  electricities. 

4.  Distribution....  (On  the  surface  of  insulated  conductors. 

I  Accumulated  at  pointed  extremities. 

fBy  conduction...  I  Keadily  in  cond^tors. 
I  Slowly  in  insulators. 

5.  Transference..  J  B?  convection  in  moving  particles. 

f  Spark. 
By  disruption... .j  Brush. 

*  Glow. 

6.  Induction By  a  charged  body  on  insulating  matter. 

I 1.  The  effects  of  statical  electricity  are : 

1.  Mechanical  ....     By  producing  fracture. 

2.  Luminous In  the  electric  spark. 

3.  Calorific  By  evolving  heat. 

4.  Chemical  j  By  decomposing  compounds. 

I  By  effecting  combination. 

5.  Magnetic By  affecting  the  magnetic  needle. 

6.  Physiological..      In  producing  shocks. 


DYNAMICAL    ELECTRICITY.  401 

DYNAMICAL    ELECTRICITY. 

708.  All  chemical  actions  are  attended  by  the  develop- 
ment of  electrical  force.     This  force  is  identical  with  that 
produced  by  friction ;  but  because  its  discharge  is  continu- 
ous, that  department  of  electrical  science  which  treats  of 
electricity  produced  by  chemical  action  is  called  dynamical 
electricity.     It  has  also  been  called  Galvanism  and    Voltaic 
electricity,  in  honor  of  Galvani  and  Volta,  who  were  among 
the  first  to  study  its  phenomena. 

709.  The   fundamental   phenomena  of  dynamical   elec- 
tricity may  be  exhibited   by  means  of  the  simple    Voltaic 
element,    Fig.    323.     This    generally 

consists  of  two  metals  plunged  in  a  f/f*   ^~ 

liquid  which  acts  upon  them  un- 
equally. The  usual  combination  is 
a  glass  vessel  containing  a  plate  of 
amalgamated  zinc*  and  a  plate  of 
copper,  partially  immersed  in  water, 
to  which  a  little  sulphuric  acid  has 
been  added.  The  chemical  action 
takes  place  only  between  the  zinc  FIG  323 

and    the    liquid,    and   may  be   thus 

explained:  (1.)  The  water  is  decomposed,  its  hydrogen  is 
liberated,  and  its  oxygen  combines  with  the  zinc  to  form 
oxide  of  zinc.  With  water  alone  this  action  is  very  feeble, 
because  the  oxide  of  zinc  soon  forms  an  insoluble  coating 
on  the  zinc  plate. 

(2.)  The  principal  use  of  the  sulphuric  acid  seems  to  be 
to  prevent  the  formation  of  this  coating.  This  it  does  by 
uniting  with  the  oxide  to  form  sulphate  of  zinc,  which 


*To  amalgamate  zinc,  it  is  first  cleaned  by  immersion  in  dilute  sul- 
phuric acid,  and  then  mercury  is  rubbed  over  its  surface.  All  zinc  em- 
ployed in  batteries  requires  to  be  frequently  amalgamated.  When  thus 
treated,  commercial  zinc  acts  precisely  as  pure  zinc;  the  amalgamation 
removes  from  its  surface  all  impurities,  and  presents  an  uniform  layer 
of  zinc  dissolved  in  mercury  to  the  action  of  the  liquid. 
N.  P.  26. 


402  NA  TURAL  PIIILOSOP1I  Y. 

readily  dissolves  in  the  liquid  and  leaves  the  plate  clean. 
The  copper  is  not  chemically  acted  upon,  and  serves  merely 
as  a  conductor. 

As  soon  as  the  plates  are  immersed,    there   is   a  slight 
disengagement  of  hydrogen   from   the  surface  of  the  zinc, 
and  both  plates  become  feebly  charged  with  electricity.     If 
the  plates  are  kept  from  touching,  no  further 
action  will  be  perceived.    The  whole  arrange- 
ment is  in  a  polarized  condition,  which  may 
be   represented   by   Fig,    324.     The   positive 
FIG  32»  molecules    are    shaded    to    distinguish    them 

from  the  negative.  The  outer  extremity  of 
the  zinc  plate  is  negative,  while  the  portion  in  contact  with 
the  liquid  is  positive.  The  negative  molecules  of  the  liquid 
are  turned  toward  the  zinc,  and  the  positive  toward  the 
copper  plate.  The  copper  thus  becomes  polarized  in  a 
sense  opposite  to  that  of  the  zinc. 

710.  If,  now,  the  plates   are  brought  in  contact,  either 
directly  or  by  means  of  a   metallic  wire,  a  discharge  will 
take  place  through  the  whole  combination,  or  circuit.     At 
the  same  time  the  chemical  action  increases,  and  gives  rise 
to  a  series  of  charges  and  discharges  in  such  rapid  succession 
that  the  discharge  is  apparently  continuous,  and  the  circuit 
is  said  to  be  traversed  by  an  electrical  current.     The  current 
continues  so  long  as  the  contact  is  maintained,  but  ceases 
when  the  wires  are  separated.     The  operation  of  connecting 
the  plates  is  called  closing  the  circuit,  and  the  separating  of 
them  is  called  breaking  the  circuit. 

711.  It  is  to  be  noted  that  when  the  circuit  is  closed,  the 
hydrogen   rises   only  from   the  surface   of  the   copper.     In 
explanation  of  this,  it  is  supposed  that  when  the  oxygen  and 
zinc  combine,  a  molecule  of  hydrogen  is  set   five,  and  unites 
with  the   oppositely  electrified    oxygen    in   the   neighboring 
molecule  of  water,  and  displaces  its  hydrogen.      This  mole- 
cule of  hydrogen  is  transferred  to  the  adjacent  molecule  of 


THE  DIRECTION   OF  THE   CURRENT.  403 

water,  and,  in  a  like  manner,  the  same  transference  takes 
place  throughout  the  whole  series,  until  the  hydrogen  of  the 
molecule  of  water  next  the  copper  is  displaced.  This  hy- 
drogen can  not  enter  into  chemical  combination  with  the 
copper,  but  discharges  its  free  positive  electricity  into  it, 
and  escapes  in  a  gaseous  state. 

Each  successive  transfer  of  the  hydrogen  may  be  assumed 
to  be  accompanied  by  a  separation  and  re-combination  of 
the  opposite  electricities.  The  current  itself  must  be  re- 
garded as  due  to  a  constant  series  of  polarization  and  dis- 
charge among  all  the  molecules  of  the  element,  both  liquid 
and  solid,  by  reason  of  which  there  is  a  transmission  of  both 
electrical  forces  throughout  the  circuit.  In  confirmation  of 
this,  we  find  that  the  circuit  manifests  the  same  effects  at 
any  point  wrhere  it  is  possible  to  test  it.  Nevertheless,  it  is 
convenient  to  use  the  term,  current,  to  designate  this  trans- 
mission of  force. 

To  avoid  confusion,  whenever  reference  is  made  to  the 
direction  of  the  current,  only  the  positive  is  indicated.  The 
direction  of  the  positive  current  (1.)  within  the  liquid,  is 
from  the  zinc  to  the  copper,  and  (2.)  without  the  liquid, 
from  the  copper  to  the  zinc.  The  negative  current  passes 
in  the  opposite  direction. 

712.  The  direction  of  the  current  is  dependent  on  the 
chemical  action,  and  is,  consequently,  influenced  both  by 
the  metals  and  the  exciting  liquid.  Within  the  liquid,  the 
current  always  sets  out  from  the  metal  most  easily  acted 
upon,  which  is,  therefore,  called  the  generating,  or  positive 
plate.  The  other  metal  is  called  the  conducting,  or  negative 
plate.  The  following  table  shows  the  electric  deportment  of 
several  substances,  with  reference  to  three  liquids,  two  of 
them  dilute  acids,  and  the  third  a  solution  of  sulphide  of 
potassium.  Each  metal  is  electro-positive  with  regard  to 
any  one  below  it  in  the  list,  and  electro-negative  with  re- 
gard to  any  one  above  it. 


404 


NATURAL   PHILOSOPHY. 


Series. 


Mhrta 

Sulpliuric  acid. 

Dilute 
II  V'lrnrhlorir  acid. 

Solution  of 
Sulphide  of  1'otassium. 

Zinc. 

Zinc. 

Zinc. 

Lead. 
Iron. 

Lead. 
Iron. 

Copper. 
Silver. 

Nickel. 

Bismuth. 

Copper. 
Bismuth. 

Antimony. 
Lead. 

Antimony. 
Copper. 
Silver. 

Nickel. 
Silver. 
Antimony. 

Bismuth. 

Nickel. 
Iron. 

In  dilute  acids,  iron  is  positive  with  respect  to  copper,  in  liquids 
containing  alkaline  sulphides,  the  order  is  inverted. 

By  dilute  sulphuric  acid  is  meant  water  to  which  from  one-eighth 
to  one-twentieth  of  its  bulk  of  acid  has  been  added.  In  all  voltaic 
elements  to  be  described,  the  electricity  is  generated  by  the  action  of 
this  acidulated  water  upon  amalgamated  zinc.  The  sulphuric  acid, 
however,  may  be  replaced  by  a  strong  solution  of  common  salt,  or  by 
weak  hydrochloric  acid,  without  loss  of  efficiency;  but  in  such  cases 
the  chloride  of  zinc  is  formed,  and  hydrogen  liberated. 

Among  tin-  most  derided  electro-negative  substances  are  silver,  car- 
bon, platinum,  and  iron  in  contact  with  strong  nitric  acid.  Either  of 
these  substances,  or  copper,  may  be  used  for  the  negative  plate. 

713.  The  electro-negative  plate  is  protected  from  chem- 
ical action,  so  long  as  it  is  in  contact  with  an  electro-posi- 
tive plate. 

Thus,  if  a  slip  of  iron  be  placed  in  hydrochloric  acid,  it  readily 
dissolves,  but  if  a  piece  of  zinc  be  laid  on  the  iron,  a  voltaic  circuit 
N  formed,  and  the  iron  will  remain  untouched  until  all  the  zinc  has 
been  corroded.  This  accounts  for  the  durability  of  "galvanized 
iron,"  which  is  iron  coated  with  zinc. 

Daw  proposed  to  apply  this  principle  for  the  protection  of  the 
copper  sheathing  of  -hips.  The  experiment  was  successful  so  far  as 
tin-  pn.tei-ti.in  of  the  sheathing  was  concerned;  but,  unluckily,  it  was 
found  that  unless  a  certain  amount  of  corrosion  takes  place  in  the 
copper,  its  surface  becomes  foul  from  the  adherence  of  marine  plants 
and  animals  and  thereby  the  sailing  qualities  of  the  vessel  are  im- 
paired. 


THE  ENERGY  OF  THE  CURRENT.       405 

714.  Poles.     The  current  passes  without  the  liquid  from 
the  negative  plate  back  to  the  positive  plate ;  hence,  if  the 
connecting  wire  be  cut,  the  positive  electricity  will  tend  to 
accumulate  at  the  end  of  the  wire  attached  to  the  negative, 
or  copper  plate,  and  the  negative  electricity  on  the  wire  at- 
tached to  the  positive  or  zinc  plate.     These  ends  or  termi- 
nals  are  called   the  poles,  or  electrodes,  of  the  circuit.     The 
name  of  the  pole  is  always  contrary  to  that  of  the  plate  to 
which  it  is   attached.     In  most  combinations  zinc  is  used 
for  the  positive  plate;    the  wire  connected  with  it  is  the 
negative  electrode  or  pole.     The  wire  attached  to  the  nega- 
tive plate  is  the  positive  electrode  or  pole. 

715.  The  energy  of  the  current  is  proportional  to  the 
chemical  activity  of  the  element,  or  to  the  amount  of  zinc 
dissolved  in    a  given   time.     It  is  greater  the  greater  the 
difference  in  the  affinity  of  the  liquid  for  the  two  metals. 

Thus,  dilute  sulphuric  acid  acts  upon  copper,  when  taken  by  itself, 
though  to  a  less  degree  than  upon  zinc ;  hence,  it  tends  to  produce  on 
the  copper  plate  a  current  acting  contrary  to  that  developed  on  the 
zinc.  The  energy  of  the  voltaic  element  is  due  to  the  difference  of  these 
two  opposing  forces.  Now,  as  dilute  sulphuric  acid  does  not  act  upon 
platinum  at  all,  a  stronger  current  may  be  established  between  zinc 
and  platinum  than  between  any  two  metals  given  in  the  series  (712). 

716.  The  quantity  of  electricity  which  a  single  voltaic 
element  can  develop,  is  proportional  to  the  size  of  its  gen- 
erating  plate.     The  quantity  is,    at   all  times,    enormous. 
It  has  been  calculated  that  an  element  which  might  be  con- 
tained in  a  lady's  thimble,  is  capable  of  evolving  a  greater 
quantity  of  electricity  than  the  largest  electrical  machine 
ever  constructed.     Nevertheless,  the  intensity  is  very  feeble. 

The  current  ceases  as  soon  as  the  circuit  is  broken,  be- 
cause it  has  not  sufficient  intensity  to  produce  a  discharge 
through  the  air.  The  enormous  quantity  but  feeble  intens- 
ity of  dynamical  electricity  afford  a  striking  contrast  to  the 
little  quantity  but  high  intensity  of  statical  electricity. 
For  the  reasons  above  indicated,  the  electroscope  can  not  be 


406  NATURAL   PHILOSOPHY. 

used,  except  in  rare  instances,  to  detect  the  current.  The 
smallest  current  may  be  at  once  detected  and  measured  by 
its  effects  on  the  magnetic  needle.  The  galvanometer  used 
for  this  purpose  is  described  in  (739). 

717.  The  intensity  will  be  increased  in  proportion  as  the 
resistance  to  polarization  and  discharge  is  increased.     The 
resistance  to  the  current  arises   (1.)   from   the  liquid  em- 
ployed in  the  element,  and   (2.)  from  the  substances  used 
to  connect  the  poles.     The  better  the  conducting  power  of  a 
substance,  the  less  will  be  the  resistance  to  be  overcome  by 
the  current. 

When  solids  are  employed,  the  resistance  increases  with  the 
length  of  tJie  conductor,  but  diminishes  as  the  area  of  its  section 
increases.  Hence,  the  shorter  and  thicker  the  connecting 
wire,  the  less  will  be  the  resistance.  The  same  law  is  approx- 
imately true  of  liquids ;  the  nearer  the  plates  are  together, 
and  the  larger  their  area,  the  less  will  be  the  resistance 
offered  to  the  current  by  the  liquid  layer  between  them. 

718.  The  conducting  power  of  different  substances,  hav- 
ing equal  dimensions  is   shown  by  the  following  table,  in 
which  silver  is  taken  as  the  standard : 


Solids. 

Silver 100. 

Copper 99.9 

Zinc 29. 

Platinum  ....  18. 

Iron 16.8 

Lead 8.3 

Carbon  ..  .04 


Liquids. 

Mercury 1.6 

Dilute  sulphuric  acid 00009907 

Strong  nitric  acid 00008868 

Common  salt,  saturated  solution 00003152 

Sulphate  of  zinc,  saturated  solution...  .00000577 
Sulphate  of  copper,  saturated  solution  .00000542 
Distilled  water  ...  .  .00000001 


From  this  it  follows,  (1.)  that  a  silver  wire  one  hundred  feet  long 
offers  less  re.-i-tanr.-  to  a  current  than  an  iron  wire  of  the  same 
thickness  si-vi -ntccn  feet  long.  (2.)  That  if  two  conductors  are  of 
equal  length,  their  conducting  power-  may  he  rendered  equal  hy 
making  the  poorer  conductor  proportionally  thicker.  Hence-,  a  thick 
bar  of  earhon  may  he  even  a  hetter  conductor  than  :t  thin  wire  of 
silver.  (3.)  That  the  resistances  offered  by  liquids  are  enormous  M 


VOLTAIC  BAT TERIES. 


407 


compared  with  solids.  Hence,  the  resistance  to  the  current,  caused  by 
the  liquid  between  the  plates,  is  ordinarily  far  greater  than  in  the 
conducting  wire.  If  the  poles  are  connected  by  short  and  thick  cop- 
per wires,  the  resistance  offered  is  practically  nothing. 

It  will  also  be  noticed  that  pure  water,  which  is  a  good  conductor 
lor  statical  electricity,  is  almost  a  non-conductor  of  the  current.  Its 
conducting  powers  are  vastly  improved  by  the  presence  of  foreign 
substances  in  solution.  This  is  one  reason  why  acidulated  water  is 
always  used  in  these  experiments. 

VOLTAIC    BATTERIES. 

719.  A  voltaic  battery  consists  of  several  voltaic  ele- 
ments, so  connected  that  the  current  has  the  same  direction 
in  all.  The  efficiency  of  the  battery  will  vary  with  the 
manner  of  grouping  the  elements.  For  the  sake  of  illus- 
tration, take  six  elements,  each  containing  a  square  inch  of 
zinc,  separated  from  a  copper  plate  by  a  liquid  layer  an 
inch  in  thickness.  If  all  similar  plates  are  connected 
together,  as  represented  in  Fig.  325,  the  effect  will  be  the 


FIG.  325. 

same  as  that  of  a  single  element  having  a  zinc  plate  of  six 
square  inches,  one  inch  distant  from  its  copper  plate.  Either 
arrangement  is  called  a  simple  voltaic  circuit. 

In  the  compound  voltaic  circuit,  the  positive  plate  of  each 
element  is  connected  with  the  negative  plate  of  the  adjoin- 


Fio.  326. 


ing  element,  as  shown  in  Fig.  326.  The  zinc  dissolved  and 
the  electricity  generated  will  be  the  same  as  in  the  simple 
circuit,  but  now  the  electrical  force  has  to  perform  addi- 


408  NATURAL    PHILOSOPHY. 

tional  work  because  the  resistance  is  increased.  For  in  the 
simple  circuit  the  spare  traversed  by  the  current  is  but  one 
thickness  of  the  liquid,  but  in  the  compound  circuit,  as 
there  is  a  separate  starting  point  in  each  element,  the  cur- 
rent must  pass  through  six  equal  thicknesses. 

The  discharge  will  not  be  effected  until  the  polarization 
rises  in  proportion  to  the  resistance  offered,  and,  conse- 
quently, the  intensity  of  the  current  will  be  increased. 
Where  the  plates  are  of  equal  size,  the  intensity  of  the 
current  is  proportioned  to  the  number  of  elements  com- 
pounded. 

A  simple  circuit  is  sometimes  called  a  quantity  battery, 

and  a  compound  circuit  an  in- 
tensity battery.  As  the  inten- 
sity is  obtained  at  the  expense 
of  the  quantity,  we  can  not 
expect  to  have  a  battery  which 
shall  at  once  exhibit  the  maxi- 
mum intensity  and  the  maxi- 
mum quantity.  For  ordinary 
FIO.  327.  purposes,  we  require  batteries 

having  some  intensity  and  con- 
siderable quantity.  This  may  be  obtained  by  first  group- 
ing the  elements  in  simple  circuits  of  two,  three,  or  more, 
and  then  connecting  the  groups  to  form  compound  circuits. 
A  good  arrangement  for  six  elements  is  represented  in 
Fig.  327. 

720.  Numerous  batteries  have  been  constructed  on  the 
principle  of  the  simple  voltaic  element,  Fig.  323,  but  most 
of  them  have  gone  out  of  use,  because  of  the  rapid  en- 
feeblement  of  their  currents. 

Thin  may  occur  (1.)  from  the  gradual  consumption  of  the  sul- 
phuric acid  and  the  /inc.  and  (2.)  from  Itx-nl  ac/iu/i.  By  local  action 
is  meant  the  production  of  -mall  closed  circuits  on  the  .-iirlace  of  the 
positive  plate,  which  are  due  to  particle-  of  lead  and  iron  adhering 
to  tlu-  /inc.  All  batteries  are  subject  to  these  defects,  which  may  be 


CONSTANT  BATTERIES.  409 

remedied,  the  former,  by  the  renewal  of  the  acid  and  the  zinc ;  and 
the  latter,  by  amalgamating  the  zinc.  When  the  zinc  is  well  amal- 
gamated, no  chemical  action  takes  place  until  the  circuit  is  closed. 

(3.)  Besides  these  defects,  the  older  batteries  were  subject  to  secondary 
currents,  acting  opposite  to  the  principal  current.  In  the  action  of  the 
simple  element,  the  hydrogen  is  apparently  evolved  from  the  copper. 
In  process  of  time  the  copper  becomes  coated  with  a  layer  of  positive 
hydrogen,  which,  of  itself,  would  weaken  the  current,  but  which  acts 
the  more  injuriously  because  it  reduces  the  sulphate  of  zinc,  and 
thereby  forms  a  layer  of  metallic  zinc  on  the  copper.  Hence,  the 
two  plates  become  gradually  less  different,  and  the  current  is  weak- 
ened. 

721.  Constant  batteries  obviate  this  last  defect  by  pre- 
venting the  permanent  deposition  of  the  hydrogen  on  the 
negative  plate.  Over  fifty  forms  of  batteries  have  been 
devised,  from  which  the  following  are  selected  for  descrip- 
tion : 

1.  One  fluid  batteries. — 1.  An  element  of  Smee's  battery 
consists  of  a  silver  plate,  placed  between  two 

plates  of  zinc,  and  suspended  vertically  in 
dilute  sulphuric  acid,  Fig.  328.  The  silver 
plate  is  coated  with  platinum  in  the  state  of  a 
fine  powder.  This  coating  renders  the  surface 
of  the  plate  rough,  and  prevents  the  adherence 
of  the  hydrogen  to  the  plate  by  its  mechanical 
action. 

In  the  other  batteries  to  be  described,  the  hydrogen          FIG.  328. 
is  removed  from  the  circuit  by  entering  into  chemical 
combination  with  the  liquid  surrounding  the  negative  plate. 

2.  The  bichromate  of  potassa  battery  resembles  Smee's  in 
its  general  appearance.      The  liquid  is   a  solution  of  ten 
parts  of  bichromate  of  potassa,  seventeen  of  sulphuric  acid, 
and  one  hundred  of  water.     The  negative  plate  is  a  cylinder 
of  carbon. 

Bunsen's  carbon  is  made  by  calcining  a  mixture  of  coke  and  bi- 
tuminous coal  in  iron  molds.  The  carbon  is  placed  either  between 
two  plates  of  zinc  or  in  the  inside  of  a  zinc  cylinder.  The  zinc  dis- 


410  NATURAL   PHILOSOPHY. 

solves  in  the  acidulated  water,  and  the  liberated  hydrogen  combines 
with  a  portion  of  the  oxygen  of  the  chromic  acid,  reducing  it  to  oxide 
of  chromium. 

This  battery  is  not  constant  in  its  action,  but  is  one  of  the  cheapest 
forms.  The  best  carbon  is  that  which  forms  on  the  interior  surface 
of  gas  retorts.  Any  one  who  can  obtain  fragments  of  this  in  a  some- 
what cylindrical  form  can  construct  a  serviceable  battery  for  himself. 
The  connections  may  be  made  by  means  of  the  binding  screws  shown 
in  the  figures,  or  by  twisting  copper  wires  tightly  about  the  upper 
portion  of  the  plates. 

3.  Small  but  very  energetic  batteries  have  recently  been 
constructed  in  a  similar  manner,  by  immersing  zinc  and 
carbon  plates  in  a  saturated  solution  of  sulphate  of  mercury. 
The  zinc  decomposes  the  water  and  liberates  hydrogen ;  the 
hydrogen  displaces  the  mercury  in  the  sulphate,  forming 
sulphuric  acid,  which  dissolves  the  oxide  of  zinc,  while  the 
effect  of  the  freed  mercury  is  to  amalgamate  the  zinc. 

722.  II.  Two  fluid  batteries.  A  simple  Voltaic  element 
may  also  be  made  of  two  solids  and  two  fluids.  The  fluids 
are  kept  from  mixing  by  means  of  a  thin  partition,  more 
or  less  porous.  The  most  efficient  substances  for  this  pur- 
pose are  animal  membranes,  like  thin  parchment  or  bladder; 
but  the  most  convenient  form  is  that  of  a  porous  cup,  made 
of  unglazed  earthen  ware.  The  porous  cup  contains  one 
liquid  and  one  plate,  and  is  placed  in  a  glass  vessel,  which 
also  contains  the  other  plate  and  the  other  liquid.  There  is 
no  fixed  order  of  arrangement;  but,  to  increase  the  size  of 
the  generating  plate,  the  zinc  is  com- 
monly cast  in  the  form  of  a  hollow  cyl- 
inder, large  enough  to  receive  the  porous 
cup  within  it,  and  is  itself  placed  in  the 
outer  glass  vessel,  together  with  dilute 
sulphuric  acid. 

4.  In  Grove's  battery,  Fig.  329,  the 
porous  cup  contains  strong  nitric  arid, 
ln  which  is  placed  a  slip  of  platinum 


TWO   FLUID   BATTERIES. 


411 


to  serve  as  the  negative  plate.     Zinc  and  dilute  sulphuric 
acid  are  placed  in  the  outer  vessel. 

The  hydrogen,  wltich  is  liberated  hy  the  action  of  the  zinc,  passes 
by  osmosis  through  the  porous  cup,  and  on  meeting  the  nitric  acid, 
unites  with  a  part  of  its  oxygen  to  form  water,  and  reduces  the  acid 
to  nitric  oxide.  This  oxide  is  either  dissolved  in  the  liquid  or  escapes 
in  deep  red  fumes,  which  are  tetroxide  of  nitrogen,  an  extremely  of- 
fensive and  poisonous  gas. 

5.  Bunsen's  battery,  Fig.  330,  is  simply  a  large  Grove's 
battery  in  which   the   platinum   slip  is 

replaced  by  a  carbon  cylinder.  The 
chemical  action  is  the  same  as  the  pre- 
ceding; but  as  the  elements  are  larger, 
for  the  same  amount  of  zinc  consumed, 
Bunsen's  battery  gives  a  greater  quantity 
but  less  intensity  than  Grove's. 

To  avoid  the  production  of  the  noxious  fumes, 
the  nitric  acid  is  frequently  replaced  by  the  so- 
lution used  in  the  bichromate  of  potassa  battery. 
Strong  brine  may  be  used  in  place  of  the  sul- 
phuric acid. 

6.  DanielVs  constant  battery,  Fig.  334,  was  the  first  devised, 
and  is  still  in  use.     It  is  more  constant  in  its  action  than 
either  Bunsen's  or  Grove's,  though  not  as  powerful.     It  may 
be  readily  constructed  by  placing  within  a  porous  cup  dilute 
sulphuric  acid  and  a  rod  of  zinc,  and,  in  the  outer  vessel, 
a  thin  roll  of  copper,  with  a  saturated  solution  of  sulphate 
of  copper.     As  the  hydrogen  is  liberated  by  the  action  of 
the  zinc,  it  enters  the  solution  of  sulphate  of  copper  and 
reduces  it,  forming  (1.)  metallic  copper,  which  is  deposited 
on  the  negative  plate,  and  (2.)  sulphuric  acid,  which  passes 
by  osmosis  through  the  porous  cup  and  replaces  the  acid 
which  was  neutralized  by  the  zinc. 

By  placing  crystals  of  sulphate  of  copper  around  the  copper  plate, 
to  replace  that  which  is  reduced,  the  action  of  the  battery  may  be 
maintained  for  months. 


FIG.  330. 


412  NATURAL    PHILOSOPHY. 

723.  III.  Other  batteries  have  been  devised  containing 
two  fluids  and  one  metal.  Grove's  gas  battery  employs 
the  oxygen  and  hydrogen  liberated  by  the  decomposition 
of  water  to  produce  secondary  currents  when  the  primary 
has  ceased.  These  batteries  are  very  interesting  in  a  theo- 
retical point  of  view,  but  as  they  are  of  little  practical  im- 
portance, no  further  description  of  them  will  be  given. 

724.  Recapitulation. 

I.  A  voltaic  element  consists  of 

r  Smee's. 

1.  Two  metals  and  one  liquid «  Bichromate. 

v  Mercurial. 
/•Grove's. 

2.  Two  metals  and  two  liquids •]  Bunsen's. 

I  Daniell's. 

3.  One  metal  and  two  fluids Gas. 

II.  The  voltaic  current  is  due, 

1.  To  the  polarization  of  the  metallic  and  liquid  particles  com- 

posing the  circuit. 

2.  To  the  contact  of  two  dissimilar  metals. 

3.  To  chemical  action  upon  one  metal. 

4.  To  a  transfer  of  the   fluid  molecules. 

III.  The  voltaic  current  is  characterized 

1.  By  its  enormous  quantity. 

2.  By  its  feeble  intensity. 

IV.  The  voltaic  circuit  may  be f  Simple. 

<-  Compound. 

THE   PHENOMENA    OF    DYNAMICAL    ELECTRICITY. 

725.  The  effects  of  the  current  are  manifested  either 
il.j  within  its  path,  or  (2.)  external  to  its  path.  The 
former  will  IK-  first  considered. 

1.  Physiological  effects.     The  science  of  dynamical  clec- 


GALVANIC    EXPERIMENT. 


413 


tricity  is  said  to  owe  its  origin  to  an  experiment  of  Galvani, 
in  1790,  which  may  be  repeated  in  the  following  manner: 

Let  a  strip  of  zinc  be  passed  below  the  crural  nerve  of  a  frog,  re- 
cently killed,  and  a  copper  wire  be  made  to  touch  the  muscles  of  the 
legs,  as  shown  in  Fig.  331. 
Each  time  the  ends  of  the 
metals  are  brought  together, 
;it  A,  the  legs  are  thrown 
out  in  the  direction  of  the 
dotted  lines.  The  same  con- 
vulsive movements  take  place 
if  one  pole  of  a  battery 
touches  the  nerves  and  the 
other  the  muscles.  The  mus- 
cles contract  as  often  as  the 
circuit  is  opened  and  closed, 
but  remain  quiet  when  the 
current  is  passing.  The  more 
frequently  and  abruptly  the 
current  is  broken  and  closed, 
the  greater  will  be  the  physi- 
ological effect.  This  remark 
also  applies  to  the  effects  of 
the  current  on  living  animals. 

If  the  electrodes  of  a  strong  battery  be  grasped  with  the 
hands,  previously  moistened,  a  shock  will  be  experienced, 
resembling  that  from  a  Leyden  jar;  but  unless  the  number 
of  elements  be  considerable,  the  sensation  is  hardly  percep- 
tible. The  nerves  of  the  palate  and  of  sight  are  easily 
affected. 

If  a  strip  of  zinc  be  placed  above  the  tongue,  and  a  silver  plate 
beneath  the  tongue,  a  peculiar  taste  will  be  experienced  when  the 
two  metals  are  made  to  touch.  If  the  silver  be  placed  between  the 
gums  and  the  cheek,  as  often  as  the  metals  are  made  to  touch,  not 
only  will  the  taste  be  perceived,  but  a  flash  of  light  will  appear  to 
pass  before  the  eye. 

By  means  of  a  very  powerful  current,  transmitted  through  animals 
recently  killed,  all  the  vital  actions  may  be  reproduced,  though  im- 
perfectly. In  some  cases  of  drowning  and  suffocation,  the  current 
has  been  used  with  success  to  restore  animation  after  it  had  been 
suspended  for  some  time. 


FIG.  331. 


414  NATURAL  PHILOSOPHY. 

726.  Calorific   effects.     When  a  voltaic  current  is  trans- 
mitted  through   a   metallic  wire,  more   or  less  resistance  is 
experienced,  which  is   dependent   both   on  the  quantity  of 
electricity  and  the  conducting  power  of  the  wire.     Heat  is 
always  developed  in  proportion  to  the  amount  of  resistance, 
as  in  the  analogous  case  of  mechanical  friction.     Hence,  if 
the  current  be  strong,  and  the  wire  an  insufficient  conductor, 
the  wire  will  be  heated,  and,  if  quite  thin,  may  become  in- 
candescent, or   even   dissipated   in  vapor.     All   the  metals 
have  been  fused  in  this  manner,  and  even  carbon  has  been 
so  softened  that  it  could  be  welded. 

When  other  conditions  are  the  same,  the  worst  conductor  will  be 
the  soonest  heated.  Thus,  if  a  suitable  current  be  passed  through  a 
chain  made  of  alternate  links  of  platinum  and  silver,  it  may  render 
the  platinum  incandescent  while  the  silver  remains  dark.  On  the 
same  principle  if  a  platinum  wire  be  interposed  in  any  part  of  the 
circuit  it  may  be  made  to  ignite  gunpowder.  As  this  can  be  done  at 
a  great  distance  from  the  battery,  and  even  under  water,  it  has  been 
turned  to  account  in  exploding  torpedoes,  and  in  blasting  rocks.  It 
has  also  been  applied  as  a  cautery  in  surgical  operations. 

727.  Luminous  effects.     No  spark  is  obtained  unless  the 
poles  are  first  brought  in  contact,  or  nearly  so.     One-twen- 
tieth of  an  inch  of  air,  or  any  other  non-conductor,  is  suffi- 
cient   to    prevent    the    discharge    of   a    battery   containing 
several  thousand  elements.     Gassiot  succeeded  in  obtaining 
sparks  .02  of  an  inch  long,  which  continued  without  inter- 
ruption, in   rapid   succession,  for  five  weeks,  but  to  obtain 
this  result  he  constructed  a  battery  of  three  thousand  five 
hundred  and   twenty  pairs  of  zinc  and  copper  plates,  insu- 
lated   with    every   possible    precaution,    and    charged    with 
water  only. 

With  a  moderately  strong  battery,  sparks  may  be  ob- 
tained at  the  moment  the  circuit  is  closed  or  broken.  If 
two  files  arc  fastened  to  the  terminal  wires,  very  brilliant 
sparks  may  be  produced  by  rubbing  the  point  of  one  over 
the  teeth  of  the  other.  A  mo-t  brilliant  cli-cfrir  H<//if  is  ob- 
tained by  connecting  the  terminals  \sitli  cylinders  of  dense 


ELECTRIC  LIGHT. 


415 


carbon,  as  shown  in  Fig.  332.     The  carbon  points  are  first 
brought   in   contact  and  the  heat    developed   is  such  as  to 
render   their   ends   incandescent.      They    may   then   be   re- 
moved to  a  short  distance  without  inter- 
rupting the  current,  which  forces  its  way 
through  the  air,  and  produces  a  luminous 
arc  of  great  intensity,  which  is  called  the 
Voltaic  arc. 

With  forty-eight  Bunsen's  elements,  the 
arc  is  about  one-fourth  of  an  inch  long. 
The  light  is  of  far  greater  intensity  than 
that  obtained  by  the  oxy-hydrogen  blow- 
pipe, being  equal  to  five  hundred  and 
seventy-two  wax  candles.  With  six 
hundred  elements,  the  arc  is  nearly  eight 
inches  long,  and  may  be  said  to  rival 
the  sun  in  brilliancy.  The  presence  of 
oxygen  is  not  necessary  to  its  formation, 
as  it  may  be  produced  in  highly  rarefied 
nitrogen,  or  other  gases,  with  nearly 
equal  brilliancy  as  in  air. 

The  light  is  not  due  to  combustion,  but 
to  the  transference  of  intensely  heated  particles  of  carbon 
from  the  positive  to  the  negative  electrode.  In  consequence 
of  this,  the  positive  electrode  gradually  wears  away,  and,  at 
the  same  time,  a  deposit  is  formed  on  the  negative  electrode. 
The  effect  of  this  is  to  increase  the  distance  between  the 
electrodes,  and  hence  some  arrangement  is  necessary  to 
bring  them  together,  in  proportion  as  the  distance  alters. 
This  may  be  done  by  the  hand,  but  is  more  effectually  ac- 
complished by  regulators  moved  by  clockwork,  and  con- 
structed so  as  to  act  automatically. 

This  apparatus  is  admirably  adapted  for  the  display  of  optical 
phenomena  in  the  class  room,  and  for  illumination  in  theaters,  but 
the  light  is  not  adapted  for  general  purposes  of  illumination.  Be- 
sides the  cost  of  its  production,  and  the  skill  required  in  its  man- 
agement, the  very  intensity  of  the  light  is  an  obstacle  to  its  use,  as  it 


FIG.  332. 


416 


NATURAL    PHILOSOPHY. 


throws  the  shadows  into  too  strong  relief,  and  acts  injuriously  upon 
the  eye. 

The  most  refractory  substances,  as  platinum,  quartz,  and  lime, 
when  introduced  within  the  voltaic  arc,  are  fused.  The  color  of  the 
light  varies  with  the  substances  placed  between  the  terminals.  Gold 
emits  a  bluish  light,  silver  an  emerald  green,  lead  a  purple,  etc. 
These  effects  are  caused  mainly  by  the  dispersion  of  the  metallic 
particles  in  vapor,  although  they  may  be  heightened  by  the  combus- 
tion of  a  portion  of  the  metals. 

728.  Chemical  effects.  If  a  chemical  compound,  in  a 
liquid  state,  be  placed  between  the  electrodes  and  made  to 
form  a  part  of  the  external  voltaic  circuit,  a  series  of  de- 
compositions will  take  place,  like  those  already  described  as 
occurring  within  the  simple  voltaic  element.  A  body  ca- 
pable of  this  decomposition  is  called  an  electrolyte,  and  the 
process  itself  is  called  electrolysis. 

Fig.  333  represents  a  very  convenient  apparatus  to  show  the  de- 
composition of  water.  It  consists  of  a  glass  vessel  having  a  cork 

bottom,  through  which  are  passed 
two  wires  terminating  in  platinum 
electrodes.  The  vessel  being  filled 
with  acidulated  water,  two  glass 
tubes,  also  filled  with  water,  are 
inverted  over  the  electrodes,  and  the 
outer  wires  are  connected  with  the 
battery.  Five  of  Grove's  or  of  Bun- 
sen's  elements  will  cause  a  rapid  de- 
composition of  the  water;  bubbles 
of  gas  will  collect  in  the  tube  above 
cadi  pole. 

On  examination,  it  is  found  that 
hydrogen  rises  from  the  negative 
pole  and  oxygen  from  the  positive. 
About  twice  as  much  hydrogen  is 
liberated  as  oxygen,  and  hence  this 
experiment  serves  both  as  a  qualitative  and  quantitative  analysis  of 
water. 

If  the  water  were  perfectly  pure,  very  little  decomposition  would 
be  effected,  because  of  the  non-conducting  properties  of  pure  water. 
If  the  conduction  wen-  perfect,  the  same  amount  of  oxygen  should  be 
set  free  in  the  tube  as  combines  with  the  zinc  in  the  battery.  By  em- 


Fio.  333. 


ELECTRO. CHEMICAL   SERIES.  417 

ploying  the  same  conductors,  but  varying  the  number  of  elements,  it 
will  be  found  that  the  gases  evolved  are  in  proportion  to  the  amount 
of  zinc  consumed ;  hence,  the  strength  of  a  battery  may  be  measured 
by  the  amount  of  water  it  can  decompose  in  a  given  time.  An  ap- 
paratus used  for  this  purpose  is  called  a  Voltameter. 

729.  The  decomposition  of  other  bodies  may  be  effected 
by  a  similar  apparatus,  provided  care  be  taken  to  make  the 
electrodes  of  some  conductor  that  is  not  attacked  by  the 
compound   or  by   any   of   its    constituents.     Hydrochloric 
acid,  for  instance,  consists  of  equal  volumes  of  hydrogen 
and  chlorine;    but  as  chlorine  attacks  all  the  metals,  the 
electrodes  must  be  of  gas  carbon. 

If  the  electrodes  be  plunged  in  solutions  of  binary  com- 
pounds, like  chloride  of  copper,  iodide  of  potassium,  the 
metals  will  collect  at  the  negative  pole  and  the  non-metals 
at  the  positive.  On  the  principle  that  bodies  dissimilarly 
charged  attract  each  other,  the  metals  are  called  electro- 
positive substances,  and  the  non-metals  electro-negative. 
An  electro-chemical  series  has  been  arranged,  in  which  any 
one  in  the  list  is  electro-negative  to  any  following  it,  but 
electro-positive  to  any  preceding  it. 

The   following  is   a   portion   of  Berzelius'   electro-chemical 

series  : 

I 

Oxygen,  Rubidium, 

Sulphur,  Potassium, 

Chlorine,  Zinc, 

Iodine,  Iron, 

Phosphorus,  Copper, 

Arsenic,  Silver, 

Carbon,  Platinum, 

Antimony,  Gold, 
Hydrogen. 
-i- 

730.  Ternary  salts  are  also  decomposed  by  the  current, 
the  metal  going  to  the  negative  pole,  and  the  acid,  or  the 
body  which  is  chemically  equivalent  to  it,  going  to  the  pos- 
itive pole. 

N.  P.  27. 


418  XATCRAL  PHILOSOPHY. 

If  a  solution  of  sulphate  of  copper  is  decomposed  by  two  copper 
electrodes,  metallic  copper  will  be  deposited  on  the  negative  pole, 
while  the  positive  pole  will  be  dissolved  to  an  equal  amount,  but  no 
gas  will  be  liberated.  If  the  positive  electrode  be  of  platinum,  bubbles 
of  oxygen  will  be  liberated  from  it,  but  copper  will  be  deposited  on 
the  negative  electrode  as  before.  To  explain  this  action,  it  is  con- 
venient to  represent  the  composition  of  sulphate  of  copper  by  the 
formula  CuSO4.  By  electrolysis,  this  is  supposed  to  divide  into  an 
electro-positive  constituent,  copper,  and  an  electro-negative  constitu- 
ent, SO4,  to  which  the  name  sulphion  has  been  given.  This  sulphion 
can  not  exist  in  a  free  state,  and  when  it  arrives  at  the  positive  elec- 
trode, a  secondary  action  takes  place,  which  is  purely  chemical.  The 
SO4  decomposes  into  anhydrous  sulphuric  acid,  SO3,  and  into 
oxygen. 

If  the  oxygen  can  enter  into  combination  with  the  electrode,  an 
oxide  is  formed  which  immediately  unites  with  the  liberated  acid 
and  dissolves  in  the  liquid ;  but  if  the  electrode  can  not  be  oxidized, 
the  oxygen  is  liberated  as  free  gas,  while  the  SO3  combines  with 
water  to  form  ordinary  sulphuric  acid  H2O,  SO3. 

Thus,  in  the  case  supposed,  if  the  positive  electrode  be  of  copper, 
it  is  first  oxidized  and  then  dissolved  as  sulphate  of  copper.  The 
solution,  therefore,  remains  of  the  same  strength,  for  as  fast  as  it  is 
decomposed  in  one  part  of  the  circuit,  it  is  reproduced  at  another. 
If  the  electrode  be  of  platinum  or  carbon,  oxygen  and  the  free  acid 
collect  at  the  positive  pole,  and  the  solution  becomes  gradually 
weaker,  from  the  abstraction  of  the  copper. 

The  decomposition  of  other  salts,  as  nitrate  of  silver,  AgNO3, 
cyanide  of  gold,  AuCy3,  or  the  cyanide  of  silver,  AgCy,  will  be 
understood  from  these  examples. 

Ordinarily,  a  single  voltaic  element  will  suffice  for  the  decomposi- 
tion of  a  salt.  The  condition  in  which  the  metal  is  deposited  on  the 
negative  electrode,  depends  to  a  considerable  degree  on  the  strength 
of  the  current.  When  the  action  is  rapid,  most  metals  are  deposited 
as  loose,  flocculent  powders;  but  if  it  is  slow,  copper,  silver,  gold, 
and  some  others,  are  deposited  in  firm,  coherent  layers,  which  ex- 
actly fit  the  surface  of  the  electrode. 

731.  Electro-metallurgy  is  the  art  of  depositing  the 
metals  from  solutions  of  their  salts,  by  means  of  the  elec- 
tric current.  The  principles  on  which  this  art  is  founded 
have  already  been  explained. 

The  solution  is  deoompowd  and  the  pure  metal  is  deposited  on  the 


ELECTRO-METALLURGY. 


419 


negative  electrode.  This  may  consist  of  any  article  whatever  that 
possesses  a  conducting  surface.  If  the  material  is  non-conducting,  the 
surface  may  be  rendered  conducting  by  covering  it  with  finely  pow- 
dered graphite,  applied  by  means  of  a  brush  of  camel's  hair.  The 
positive  electrode,  C,  Fig.  334,  should  be  a  plate  of  the  same  metal 
as  that  to  be  deposited,  in  order  that  it  may  be  dissolved  by  the  acid 
which  is  liberated,  and  thus  maintain  the  strength  of  the  solution. 

732.  The  processes  of  electro-metallurgy  may  be  ar- 
ranged in  two  divisions:  (1.)  those  in  which  the  deposit 
remains  permanently  fixed  on  the  electrode;  (2.)  those  in 
which  the  deposit  is  intended  to  be  removed.  The  first 
may  be  represented  by  electroplating,  and  the  second  by 
electrotyping. 

Electroplating.  The  apparatus  employed  in  electro- 
plating is  represented  in  Fig.  334.  The  bath  consists  of  a 


'Ln 


FIG.  334. 

weak  solution  of  cyanide  of  silver.  The  articles  to  be  sil- 
vered are  first  carefully  cleaned,  then  attached  to  the  nega- 
tive pole  of  the  battery  and  immersed  in  the  bath.  A 
coating  of  pure  silver  begins  to  form  at  once,  and  may  be 
obtained  of  any  thickness  desired.  When  the  articles  are 
first  taken  from  the  bath  their  surfaces  appear  dull  and 
white.  The  metallic  luster  of  silver  is  then  communicated 
to  them  by  polishing  and  burnishing. 


420  NATURAL   PHILOSOPHY. 

By  a  similar  process,  articles  may  be  electro-gilded,  or  coated  with 
copper,  nickel,  and  several  other  metals.  When  iron,  tin,  zinc,  or 
Britannia  metal  are  to  be  electroplated  or  gilded,  the  articles  must 
first  be  electro-coppered  in  order  to  secure  the  adhesion  of  the  silver 
or  the  gold.  All  solutions  do  not  deposit  equally  well;  the  soluble 
chlorides  are  generally  employed;  gold  and  silver  are  deposited  from 
their  cyanides;  copper,  as  a  general  thing,  from  its  sulphate. 

733.  Electrotyping.      When   a   medal   has   been   electro- 
coppered,  the  coating,  if  sufficiently  thick  to  be  stripped  off 
whole,  will  give  a  surface  the  exact  reverse  of  the  medal, 
even  to  the  finest  lines.     If  this  reversed  copy,  or  mold,  be 
attached  to  the  negative  electrode,  a  second  copy  may  be 
formed    which    will    exactly    resemble    the    original.     Any 
object  may  be  copied  in  this  manner,  but,  in  the  ordinary 
processes  of  electrotyping,  it  is  usual  (1.)  to  form  a  mold 
of  the  object  in  wax,  gutta-percha,  or  plaster,  and  (2.)  then 
to  deposit  within   this  a  sufficiently  thick  coating  of  some 
metal,  which  is  usually  copper. 

Thus,  suppose  we  desire  to  copy  a  medal  in  copper.  It  is  first 
rubbed  over  with  graphite,  and  the  excess  of  graphite  blown  off'; 
then  (2.)  an  impression  is  taken  in  wax,  and  the  wax  coated  with 
graphite  as  before;  (3.)  a  copper  wire  is  now  thrust  through  the  wax 
and  made  to  connect  with  tin.-  layer  of  graphite;  finally,  (4.)  it  is 
made  the  negative  electrode  in  a  bath  of  sulphate  of  copper.  A 
tough  coat  of  copper  will  gradually  be  deposited  on  the  surface  of 
the  graphite,  and  after  a  day  or  two  will  be  sufficiently  thick  to  be 
removed.  The  plates  from  which  this  book  was  printed  were  elec- 
trotyped  by  this  process. 

734,  The  student  may  easily  copy  seals,  coins,  and  other 
small  articles,  without  the  aid  of  a  battery,  by  the  simple 
means  shown  in  Fig.  335.     A  is  a  glass  vessel  containing 
a  saturated   solution   of  sulphate  of  copper;    B  is  a  lamp 
chimney,  closed  below   with   a  piece  of  bladder,  and  con- 
taining very  dilute  sulphuric  acid.     The  apparatus  is  com- 
pleted  by  putting  a   mil   nf  amalgamated    zinc    in   the   sul- 
phuric  acid,   and    connecting  it   by  a   wire  to  the  object  to 
be  copied,   which    is    laid    below    tin-   bladder.     The  combi- 
nation   is    evidently    equivalent     to    a    .-ingle    element    of 


CURRENT  INDUCTION.  421 

Daniell's  battery.     The  connecting  wire,  and  any  part  of 
the  object  which   it  is  not 
desired    to   copy,   must  be 
carefully  coated  with   wax 
or  some  resinous  varnish. 

The  applications  of  electro- 
typing  are  very  numerous.  By 
means  of  it  engraved  plates, 
wood  cuts,  seals,  bas  reliefs,  and 
other  objects  may  be  reproduced 
in  copper,  and  an  unlimited 

number  of  copies  obtained  with-  FIG.  335. 

out  injuring  the  original  in  the  lea^t. 

735.  Recapitulation. 

The  effects  of  the  current  within  its  path  are: 

1.  Physiological Applied  in  disease. 

2.  Calorific Applied  in  firing  mines. 

3.  Luminous Applied  in  the  electric  light. 

4.  Chemical Applied  in  electro-metallurgy. 

PHENOMENA  EXTERNAL  TO  THE  PATH  OF  THE  CURRENT. 

736.  The  voltaic  current  also  acts  inductively  upon  con- 
ductors external  to  its  path,  and  thereby  causes  phenomena 
which  closely  ally  its  action  to  magnetism.  These  phenom- 
ena may  be  grouped  in  two  divisions : 

1.  Electro-magnetism  considers   the   phenomena   in   which 
magnetic  attraction  and  repulsion  are  caused  by  the  voltaic 
current. 

2.  Electro-dynamic  induction  considers  the  production  of 
other  currents  in  the  vicinity  of  closed  circuits. 

It  is  also  found  that  permanent  magnets  may  act  induc- 
tively on  conducting  wires,  and  thereby  give  rise  to  electrical 
currents  without  the  aid  of  a  battery.  The  study  of  these 
phenomena  belongs  to  magneto-electricity. 


422 


NATURAL   PHILOSOPHY. 
ELECTRO-MAGNETISM. 


737.  Oersted  discovered,  in  1819,  that  a  magnetic  needle 
held  in  the  vicinity  of  a  voltaic  current,  tends  to  place 
itself  at  right  angles  to  the  conducting  wire. 

To  repeat  his  experiment,  a  magnetic  needle  is  placed  on  a  pivot 
and  allowed  to  assume  its  natural  position  in  the  direction  of  the 
magnetic  meridian.  If,  now,  the  conducting  wire  of  a  voltaic  current 


FIG.  336. 

be  held  parallel  to  the  needle ;  the  needle  will  be  deflected  and  ulti- 
mately assume  a  position  which  is  more  nearly  at  right  angles  to  the 
magnetic  meridian,  as  the  current  is  more  intense. 

738.  The  direction  in  which  the  needle  should  turn,  may 
be  remembered  by  the  following  rule,  devised  by  Ampere: 

Suppose  a  diminutive  figure  of  a  man  to  be  so  placed  in  the 
circuit  that  the  current  shall  enter  by  his  feet  and  leave  by  his 
head ;  then,  if  his  face  be  always  turned  toward  the  needle,  its 
north  pole  will  be  deflected  toward  his  left. 

In  accordance  with  this  rule,  if  the  current  passes  above  the  needle 
and  goes  from  south  to  north,  the  north  pole  of  the  needle  will  be 
deflected  toward  the  west.  The  same  deflection  will  take  place  if  the 
current  passes  below  the  needle  from  north  to  south. 

Hence,  if  the  wires,  N  S,  N'  S',  be  connected  so  that  the  current 
shall  |>:i--  anuniil  tin-  m-i-dli-,  the  deflecting  power  of  the  current  will 
be  doubled.  By  coiling  the  wire  se\vral  times  around  the  needle, 
provided  that  the  coils  are  insulated  from  each  other,  the  deflecting 


GAL  VANOMETER. 


423 


power  of  the  current  will  be  so  multiplied  that  the  needle  may  be 
used  to  detect  the  presence  of  very  weak  currents,  to  determine  their 
direction,  and  even  to  measure  their  intensity.  An  instrument  con- 
structed on  this  principle  is  termed  a  galvanometer. 

739.  The  sensibility  of  the  galvanometer  may  also  be 
increased  by  the   use  of  an  astatic  needle.     This  consists  of 
two  magnetic  needles,  Fig.  337,  fast- 
ened in  the  same  axis  of  suspension, 
but    with    their    poles    reversed.       If 
these  are  suspended  by  a  silk  thread, 
so  that  one  needle  swings  freely  within 
the  coil  and  the  other  above  it,  they  constitute  the  astatic 


S'- 


-N' 


FIG.  337. 


FIG.  338. 


galvanometer,  shown  in  Fig.  338.  The  advantages  of  this 
instrument  are:  (1.)  the  directive  force  of  the  earth  on  the 
needle  may  be  almost  neutralized,  because  the  poles  of  the 


424  X AT  URAL  PHILOSOPHY. 

needles  lie  in  opposite  directions.  (2.)  The  force  of  the 
coil  is  exerted  in  the  same  direction  upon  two  needles  in- 
stead of  one.  For,  although  the  upper  needle  is  subject  to 
the  action  of  two  opposite  currents,  yet  as  that  in  the  upper 
part  of  the  coil  is  much  the  nearer,  its  action  prepon- 
derates, and,  because  the  needles  are  reversed,  both  are 
deflected  in  the  same  direction. 

The  wire  used  in  this,  and  in  other  coils,  should  be  carefully  insu- 
lated, by  being  covered  with  white  silk  thread.  A  coil  having  a  few 
hundred  turns  of  moderately  thick  copper  wire  is  well  adapted  for 
ordinary  experiments ;  but,  for  very  delicate  investigations,  as  many 
as  thirty  thousand  turns  of  fine  wire  have  been  used. 

740.  If  the  conducting  wire  be  movable  we  may  obtain 
results  the  converse  of  the  preceding.     That  is,  a  straight 
conducting  wire  will  tend  to  place  itself  at  right  angles  to 
a  magnet  held  in  its  vicinity. 

De  la  Rive's  floating  battery,  Fig.  339,  will  enable  us  to  verify 
this  fact,  as  well  as  to  exhibit  other  properties  of 
the  current.  It  consists  of  a  small  voltaic  ele- 
ment, which  is  floated  in  acidulated  water  by 
means  of  a  cork  attached  to  its  upper  end.  The 
conducting  wire  may  be  made  straight,  rect- 
angular, or  coiled.  The  spiral  coil  shown  in  the 
figure  is  technically  called  a  helix.  An  elongated 
helix,  with  its  conducting  wire  returned  through 
the  axis  of  the  coil,  is  a  solenoid,  Fig.  341.  The 
coil  is  right-handed,  when  its  spire  winds  to  the 
right,  like  a  corkscrew,  and  is  left-handed  when 
its  spire  winds  in  the  opposite  direction. 

741.  By  means  of  this  apparatus,  it  may  be  shown  that 
when  a  current  is  passing  through   the  wire,  it  exhibits  all 
the  properties  of  a  magnet. 

1.  If  a   permanent    magnet  be  held   near  the   helix,  one 
f'aee  of  the  coil   will  l>e  attracted  by  the  north  pole  of  the 
magnet,  and  the  other  repelled. 

2.  Kadi  >idc  of  the  helix  will  attract  iron  filings. 

3.  If  a    helix    01-  solenoid    he    free  to  move,   it   will  swing 
so  that  its  axis    points  north  and  south.     If  the  coil   be 


SOLENOIDS. 


425 


right-handed,  the  south  pole  will  be  the  end  at  which  the 
current  enters;  but  if  the  coil  be  left-handed,  the  north 
pole  will  be  the  end  at  which  the  current  enters. 

4.  If    the    conducting    wire    of  the    floating    battery  be 
straight,  and  a  wire  from  another  circuit  be  placed  parallel 
to  it:   (1.)   The  wires  will  be  mutually  attracted  if  the  currents 
pats  in  the  same  direction,  but  (2.)  will  be  repelled  if  the  cur- 
rents pass  in  contrary  directions. 

The   attraction   of  similar  currents   may   be   shown    by 
means  of  a   spiral   of   fine   copper  wire,   connected   at  its 
upper  end  with  the  positive  pole  of  a 
battery,   and   slightly   dipping,  at  its 
lower  extremity,  in  a  cup  of  mercury, 
which  is  in  connection  with  the  nega- 
tive pole.     When  the  current  passes, 
each   turn   of  the   spiral  attracts  the 
next,   thereby    shortening    the    spiral, 
and  breaking  the  current  with  a  spark.  f  IG-  340. 

The  weight  of  the  wire  then  restores 

the  connection,  and  thus  a  continuous  oscillation  is  sus- 
tained. 

5.  If  twro  solenoids  are   brought  near  each  other,   Fig. 


FIG.  341. 


341,  with  their  similar  ends  adjacent,  they  will  repel  each 
other,  because  the  currents  of  the  two  coils  are  in  opposite 


426 


NATURAL    PHILOSOPHY. 


FIG.  342. 


directions.  Conversely,  the  dissimilar  ends  will  attract 
each  other. 

742.  Electro-magnetic  rotation.     We  have  seen  that  the 
current  acts  at  right  angles  to  a  magnet,  and  tends  to  urge 

the  north  pole  of  a  magnet  always 
toward  the  left.  Hence,  it  is  pos- 
sible so  to  arrange  the  connecting 
wire  and  the  magnet,  that  one 
shall  revolve  about  the  other. 
There  are  many  contrivances  for 
accomplishing  this,  one  of  which 
is  shown  in  Fig.  342. 

E  and  F  are  two  glass  cups  containing 
mercury.  A  B  C  is  a  conducting  wire, 
jointed  at  D,  and  dipping  at  each  end  in 
the  mercury.  N  S,  Nx  S',  are  two  bar 

magnets,  one  fixed  and  the  other  attached  by  a  thread  to  the  bottom 
of  its  cup.  If,  now,  a  current  is  passed  through  the  mercury  and  the 
conducting  wire,  there  will  be  a  mutual  repulsion  between  the  ends 
of  the  magnets  and  the  conducting  wire.  The  magnet,  N  S,  being 
free,  will  revolve  about  the  end,  A,  of  the  wire;  but  in  the  other  cup, 
as  the  magnet  is  fixed  and  the  wire  free,  the  wire  will  revolve  about 
the  magnet,  W  S'.  When  the  current  passes  in  the  direction  of  the 
arrows,  both  rotations  will  be  to  the  left;  but  if  the  current  is  passed 
in  the  opposite  direction,  the  rotations  will  be  to  the  right. 

743.  The  voltaic  current  may  also  induce  magnetism  in 
magnetic  substances.     If  a  bar  of  soft  iron,  N  S,  be  placed 
in  the  axis  of  a  helix,  so  that  the  current  may  pass  at  right 

angles  to  its  length,  the  bar  will  be 
instantly  magnetized,  but  will  lose 
its  magnetism  as  soon  as  the  cur- 
rent ceases.  If  the  helix  is  held 
vertically  while  the  current  is  pass- 
ing, the  bar  will  not  fall  out.  If 
the  bar  be  pulled  down  a  little  way 
and  then  let  go,  it  will  spring  back 
With  a  powerful  current  and  a 


no.  MS. 


to  its   former  position. 


ELECTS  0-MA  GNETS.  427 

large  coil,  a  weight  of  several  hundred  pounds  may  be  sus- 
pended from  the  bar,  and  the  whole  sustained  without  any 
visible  support. 

A  pleasing  modification  of  the  same  experiment  may  be  had  by 
joining  the  ends  of  two  semicircular  pieces 
of  soft  iron,  with  one  pair  of  the  ends  within 
the  helix,  as  shown  in  Fig.  344.  While  the 
current  is  passing  they  will  adhere  with 
considerable  force. 

744.  Electro-magnets    are    bars   of  FlG- 344- 

soft  iron  which  become  magnets  under  the  influence  of  the 
voltaic  current. 

Electro-magnets  of  surprising  power  have  been  made  by 
bending  bars  of  soft  iron  in  the  form  of  a  horse-shoe,  and 
surrounding  each  leg  with  many 
coils  of  insulated  copper  wire. 
When  a  strong  current  is  passed 
through  the  wire,  the  magnetism 
induced  is  far  greater  than  is  pos- 
sible in  a  permanent  magnet. 
Electro-magnets  have  been  made 
that  were  capable  of  sustaining 
nearly  two  tons. 

The  polarity  of  an  electro-mag-  FlQ 

net  depends  upon  the  direction  in 

which  the  current  moves  in  the  helix.  If  the  direction  be 
reversed  the  polarity  will  be  reversed.  If  the  current  is 
broken  the  magnetism  almost  instantly  ceases. 

745.  Permanent  magnets.     If  the  iron  employed  in  elec- 
tro-magnets is  not  quite  pure,  it  will  retain  traces  of  mag- 
netism for  some  time  after  the  circuit  is  broken.     A  steel 
bar  placed  in  the  helix,  Fig.  343,  will  become  permanently 
magnetized. 

It  is  sufficient  to  move  the  bar  once  nearly  through  the  coil,  then 
backward  till  it  lies  in  the  center  of  the  coil ;  the  current  is  then 
stopped  and  the  bar  taken  out.  A  better  result  will  be  attained,  if 


428  NATURAL   PHILOSOPHY. 

the  bar  be  previously  armed  with  short  cores  of  soft  iron,  which  just 
fit  the  ends  of  the  helix.  This  method  may  also  be  applied  to  horse- 
shoe magnets  of  steel. 

Permanent  horse-shoe  magnets  may  be  made  of  steel 
wrought  in  the  proper  shape,  by  connecting  their  open  i-nds 
with  a  keeper  of  soft  iron,  while  an  electro-magnet  is  passed 
along  a  few  times  from  the  poles  to  the  bend. 

A  better  method  is  that  shown 
in  Fig.  346.  The  steel  horse- 
shoe is  applied  to  the  electro- 
magnet, and  a  piece  of  soft  iron 
is  drawn,  in  the  direction  of  the 
arrow,  beyond  the  curve,  and  is 
then  replaced  and  the  process 

repeated.  Both  magnets  are  then  turned  over  without  separating  the 
poles,  and  the  other  side  treated  in  the  same  way.  Magnets  have 
been  made  in  this  manner  so  as  to  be  capable  of  sustaining  twenty- 
six  times  their  own  weight. 

746.  Ampere's  theory  of  magnetism.  In  view  of  these 
various  magnetic  properties  of  the  current,  Ampere  as- 
sumes that  all  bodies  which  exhibit  polarity  derive  this 
polarity  from  electrical  currents,  which  are  perpetually 
traversing  each  molecule  of  a  magnetic  substance.  Mag- 
netization consists  in  giving  to  these  individual  currents  a 
parallel  direction.  When  all  the  currents  are  parallel,  the 
magnet  is  said  to  be  saturated. 

The  resultant  of  these  parallel  currents  is  equal  to  a 
single  current  which  traverses  the  outside  of  a  magnet  as  if 
it  were  a  solenoid.  At  the  north  end  of  a  magnet,  the 


FIG.  317. 


direction  of  these  current.-  is  opposite  to  that  of  the  hands 
of  a  watch,  and  at  the  south  end  the  direction  is  the  same 


ELECTRO-MAGNETIC  MACHINES. 


429 


as  that  of  the  hands.     In  this  view  of  the  subject,  magnet- 
ism is  a  branch  of  dynamic  electricity. 

This  theory  does  not  assign  a  reason  for  the  persistence  of  currents 
in  permanent  magnets,  but  in  other  respects  affords  a  satisfactory  ex- 
planation of  all  magnetic  phenomena.  For  instance,  it  explains  why 
like  poles  attract  and  unlike  repel.  If  two  south  poles  are  brought 
near  each  other,  they  have  opposite  currents  on  their  adjoining  sides, 
and  hence  repel.  A  north  and  south  pole  have  similar  currents  on 
their  adjoining  sides,  and  attract. 


ELECTRO-MAGNETIC    MACHINES. 


747,  Various  machines  have  been  devised  in  the  hope 
of  employing  the  prodigious  force  of  electro-magnets  as  a 
motive  power.  All  of  these  take  advantage  of  the  facility 
with  which  the  polarity  of  an  electro-magnet  may  be  an- 
nulled or  reversed,  by  which  attractions  and  repulsions 
may  be  so  arranged  with  another  magnet  as  to  produce  a 
rotary  or  alternating  motion. 

The  action  of  the  first  class  may  be  illustrated  by  Page's 
revolving  electro-magnet,  Fig.  348. 

A  small  electro-magnet,  H,  is  fixed  to  a 
vertical  shaft  so  as  to  revolve  between  the 
poles  of  a  permanent  horse-shoe  magnet. 
The  ends  of  the  wires  of  the  helix  are  sol- 
dered to  two  strips  of  silver  on  opposite  sides 
of  the  shaft,  insulated  from  each  other  and 
from  the  shaft.  Two  metallic  springs,  Z,  C, 
connecting  with  the  battery,  are  so  placed 
that  when  the  shaft  makes  half  a  revolution, 
the  silver  strips  pass  from  one  spring  to  the 
other.  This  reverses  the  direction  of  the 
current  in  the  helix,  and  thereby  causes  the 
poles  of  the  electro-magnet  to  be  changed 
twice  in  each  revolution. 

The  position  of  the  two  magnets  is  such 

that,  during  the  first  quarter  of  a  revolution,  their  like  poles  are 
adjacent  and  repel;  during  the  second  quarter,  their  unlike  poles 
approach  and  attract.  The  current  is  then  reversed,  like  poles  again 
face  each  other  and  are  repelled.  The  shaft  is  thus  made  to  rotate, 


Fio.  348. 


430  NATURAL   PHILOSOPHY. 

ami  may  be  made  to  communicate  motion  to  a  train  of  wheels,  so  that 
the  rate  of  motion  may  be  accurately  determined.  The  velocity 
attained  by  this  machine  has  reached  as  high  as  2500  revolutions  per 
minute. 

No  electro-magnetic  engines  have  been  or  can  be  devised  which 
can  compete  with  steam  engines  in  economy,  because  the  expense  of 
the  zinc  and  the  acid  consumed  in  the  battery  far  exceeds  that  of  the 
coal  burned  in  steam  boilers  of  the  same  power.  Nevertheless,  small 
electro-magnetic  engines  have  been  employed  successfully  in  cases 
where  economy  is  of  less  consequence  than  convenience  and  facility  of 
application. 

748.  The  electric  telegraph  is  by  far  the  most  important 
application   of  electricity   to   the    practical   affairs    of  life. 
Very  many  forms  of  this   telegraph   have  been  invented, 
but    every    electric    telegraph    consists    essentially   of   four 
parts:    (1.)    a   voltaic  battery   for   generating   a    current; 
(2.)  a  circuit  consisting  of  an  insulated  metallic  connection 
between  two  places;   (3.)  a  key,  which  is  an  instrument  for 
sending  signals  from  the  one  station,  and  (4.)  an  instrument 
for  receiving  signals  at  the  other  station. 

Any  constant  battery  may  be  used  for  generating  elec- 
tricity. In  this  country,  Grove's  and  Daniell's  are  both  in 
use.  Twenty-five  Grove's  elements  are  required  for  a  line 
of  one  hundred  miles. 

The  line  circuit.  Two  stations  must  be  connected  by 
at  least  one  insulated  metallic  wire.  Generally  speaking, 
this  is  done  by  passing  galvanized  iron  wires  over  glass  in- 
sulators attached  to  a  series  of  tall  wooden  posts.  When 
the  wire  is  to  be  laid  in  the  sea,  or  under  ground,  it  is  in- 
sulated by  being  coated  with  gutta-percha. 

749.  The  earth  circuit.     At  the  station  which  sends  the 
dispatch  the  line  is  connected  with  the  positive  pole  of  the 
battery ;    but   as   the  current  will   not  pass  unless  the  two 
pol^s  of  the.  battery  are  connected,  it  is  necessary  to  have 
a  second   conductor    n-timnn<r  in  the  opposite  direction   to 
the  negative  pole  of  the  battery. 


MORSE'S   TELEGRAPH,  431 

In  1837,  Steinheil  discovered  that  the  earth  itself  might 
ho  used  for  the  return  conductor.  To  effect  this,  large 
copper  plates  are  buried  in  the  ground  at  each  station,  and 
are  connected  at  the  sending  station  with  the  negative  pole 
of  the  battery,  and,  at  the  receiving  station,  with  the  line 
wire.  The  earth  really  dissipates  the  electricity,  but  the 
eifect  is  the  same  as  if  it  were  an  infinitely  large  return 
conductor  offering  an  infinitely  small  resistance. 

750.  Wheatstone's  needle  telegraph,  which  is  extensively 
used  in  England,  consists  essentially  of  a  delicate  galvanom- 
eter placed  at  the  receiving   station,  and   a  pole   changer 
placed  at  the  other  station.     By  means  of  this  pole  changer, 
or  key,  the  direction  of  the  current  is  reversed,  and  the 
needle  of  the  galvanometer  made  to  deflect  to  the  right  or 
to  the  left  at  the  pleasure  of  the  operator.     A  set  of  signals 
may  in  this  manner  be  transmitted  from  one  station  to  the 
other.     With  this  system,  two  deflections  of  the  needle  to 
the  left  represent  A ;  two  to  the  right,  N ;  one  to  the  right 
and  two  to  the  left,  E ;   and  so  on   for  other  letters  and 
figures. 

A  modification  of  this  telegraph  is  used  with  the  Atlantic  subma- 
rine cable.  Although  its  sensitiveness  makes  it  a  necessity  on  very 
long  circuits,  yet  it  affords  no  means  of  registering  the  dispatches 
sent,  nor  of  detecting  errors  in  copying  the  signals. 

751.  Morse's  telegraph,  which  is  more  extensively  used 
than    any  other,    prints  the   signals   on   a  strip  of  paper. 
This  instrument  requires  at  least  two  distinct  parts :   (1.)  a 
signal  key;  (2.)  a  recording  apparatus,  or  receiver.     (3.)  Be- 
sides these,  a  third  part,  called  a  relay,  is  necessary  on  long 
circuits,  as  an  adjunct  to  the  receiver.     These  parts  are  all 
shown  in  Fig.   351.     If  messages  are  to  be  received  and 
answered,    each    station    will    require    both    a   key   and    a 
receiver. 

752.  The  signal  key  is  used  for  breaking  and  closing  the 
circuit  at  the  transmitting  station.    This  may  be  effected  by 


432  NATURAL   PHILOSOPHY. 

flitting  the  line  wire,  and  alternately  joining  and  separating 
the  two  ends  thus  formed ;  but  for  the  sake  of  convenience 
it  usually  has  the  form  represented  in  Fig.  351. 

This  consists  of  a  brass  lever,  ad,  which  works  on  an  axis,  K,  sup- 
ported by  an  insulated  base.  The  middle  of  the  lever  is  always  in 
connection  with  the  line  wire;  at  the  ends  are  two  metallic  points,  by 
which  the  line  wire  may  be  brought  in  connection  either  with  the 
receiver  or  with  the  positive  pole  of  a  battery. 

(1.)  When  the  lever  is  left  to  itself,  a  spring,  n,  forces  the  end,  «, 
down,  so  that  the  receiver  at  B/  is  in  condition  to  receive  a  dispatch 
from  a  distant  station.  (2.)  When  a  dispatch  is  to  be  transmitted,  the 
end,  d,  is  depressed  by  applying  the  finger  to  an  ebonite  button,  /,  and 
the  current  passes  from  the  battery  up  the  point,  d,  through  the  lever 
to  K,  and  along  the  line  wire  to  the  receiving  instrument  (or  relay) 
at  the  distant  station,  and  thence  returns  by  the  earth,  making  the 
circuit  complete.  When  the  finger  is  removed,  the  current  ceases,  and 
hence  the  operator  can  close  the  circuit  for  a  longer  or  shorter  time, 
at  his  pleasure,  by  depressing  or  elevating  the  end,  d. 

753.  The  receiver,  Fig.  349,  consists  (1.)  of  an  electro- 
magnet whose  helices  form  a  part  of  the  line  circuit,  and 
(2.)  of  a  lever  which  is  operated  by  the  joint  action  of  the 
electro-magnet  and  an  adjustable  spring. 


One  end  of  the  coil,  L.  i-  connected  with  the  line  wire  from  the 
s.-ndin.i;  station,  mid  tin-  other,  K,  with  the  earth.  When  the 
circuit  is  closed,  the  electro-magnet  draw.-  down  the  armature,  A, 


THE  RELAY.  433 

which  is  so  attached  to  a  horizontal  lever  that  when  the  end  A  is 
depressed,  the  other  end,  P,  is  forced  up.  This  end  carries  &  steel 
point,  or  style,  which  writes  the  signals. 

For  this  purpose,  a  narrow  slip  of  paper  is  drawn  by  clock  work 
between  the  style  and  a  revolving  cylinder,  and  is  indented  by  the 
pressure  of  the  style.  When  the  circuit  is  broken,  the  style  is  pulled 
down  by  the  spring  and  the  paper  left  blank.  Hence,  by  varying  the 
time  of  contact  at  the  sending  station,  a  series  of  signals,  formed 
by  dots  and  lines,  can  be  produced  at  the  receiving  station. 

The '  following  is  the  modified  Morse's  alphabet,  now  in 
general  use  throughout  the  world: 


a  6  c  d         e          f  g  h          i         j 

k  I  mnopqrst 

u          v  w  x  y  z  &  12 

34567  89  0 


754.  The  clicking  sound  of  the  armature  and  the  style 
indicates  to  the  ear  the  same  distinction  of  long  and  short 
signals,  that  are  indicated  to  the  eye  upon  the  paper.      A 
skillful  operator  seldom  looks  at  the  paper  when  he  is  re- 
ceiving a  message,  but  reads  only  by  sound. 

755.  The  relay.     The  intensity  of  the  current  is  so  weak- 
ened after  it  has  traversed  a  few  miles,  that  the  recording 
instrument  can  be  worked  directly  by  the  line  current  only 
on   short  circuits,  generally  not  exceeding  fifty  miles.      In 
longer  circuits,  the  actual  receiving  instrument  is  the  relay. 
This  is  simply  an  electro-magnet,  whose  only  duty  is  to  open 
and  close  a  local  circuit,  in  which  the  recording  instrument 
is  included. 

The  manner  in  which  this  is  effected  will  be  rendered  evident  by 
an  inspection  of  Fig.  350.     The  line  current  passes  from  the  positive 
pole  of  the  battery,  through  the  key  and  the  line  wire  to  the  relay, 
X.  P.  28. 


434 


.\ATURAL  PHILOSOPHY. 


thence  around  the  helices  of  the  relay  and  down  to  the  earth  plate, 
X.  The  earth  connection  is  then  said  to  return  the  current  to  the 
ground  plate,  X",  and  thus  finally  completes  the  circuit  to  the  zinc 
pole  of  the  battery. 


xeiver    A,  /HH 


FIG.  350. 

Each  time  the  line  current  passes  into  the  relay,  the  electro-magnet 

attracts  its  armature,  A,  which  is  fixed  at  the  bottom  of  a  vertical 
lever,  L.  At  the  same  time  the  upper  end  of  the  lever  strikes  against 
the  screw,  P.  At  this  moment  a  current  from  a  local  battery,  B', 
enters  at  the  axis  of  the  lever,  ascends  to  the  screw,  P,  thence  passes 
to  the  electro-magnet  of  the  recording  instrument,  and  finally  returns 
to  the  local  battery  from  which  it  started.  When  tin-  line  current 
ceases,  the  lever  is  drawn  back  by  the  spring,  S,  and  the  local  cir- 
cuit is  broken.  By  this  means,  the  local  current  is  made  to  act  in 
unison  with  the  line  current,  and  may  be  used  either  to  print  a 
legible  dispatch,  or  to  transmit  a  fresh  current  to  another  station 
further  on. 

756.  The  electric  fire  alarms  now  extensively  used  in 
large  cities  for  indicating  the  locality  of  fires,  are  modifica- 
tions of  the  Morse  instrument. 

A  number  of  stations  are  connected  with  a  central  station  by 
means  of  a  single  wire,  which  leads  from  the  positive  pole  of  a 
battery  back  to  the  negative  pole.  At  each  station  is  a  signal  box, 
so  arranged  that  by  turning  a  crank  within  tin-  hox  the  circuit  is 
opened  and  closed  a  number  of  time-,  em-responding  to  the  number 
of  the  station,  and  the  alarm  of  lire  telegraphed  to  the  central  sta- 


THE  TELEPHONE.  435 

tion.  The  watchman  at  the  central  station,  on  receiving  this  alarm, 
indicates  the  locality  to  the  si-venil  fire-engine  companies  by  means 
of  bells,  which  are  struck  as  often  as  the  circuit  which  passes  around 
the  electro-magnet  is  broken. 

A  similar  apparatus  is  frequently  used  in  large  manufactories  for 
conveying  signals  from  one  part  of  the  establishment  to  another. 

757.  The    properties    of  the    electro-magnet   have   also 
been  practically  applied  to  various  purposes.     Among  these 
are  electric  pendulums,  electrw  clocks,  and  chronographs.     The 
chronograph    is   an   instrument   for    recording    the    time   at 
which  any  phenomenon  occurs. 

758.  Various   other   telegraphs   have  been    devised,   of 
greater  or  less  merit.     Two  of   these,  invented   by  R.   E. 
House,  in  1848,  and  by  D.  E.  Hughes,  in  1855,  print  the 
message  as  received,  in  plain  Roman  letters. 

In  Caseli's  pantelegraph,  the  message  is  written  on  tin 
foil  with  wax  varnish,  and,  by  a  very  ingenious  apparatus,  is 
reproduced  in  exact  counterpart  at  the  distant  station,  on 
paper  chemically  prepared.  By  this  means,  not  only  may 
autographic  messages  be  transmitted,  but  even  engravings 
may  be  copied. 

759.  The  Telephone  transmits  sound  waves  to  a  distant 
station.     So  perfect  are  some  of  the  recent  inventions  that 
conversation  has  been  possible  at  great  distances. 

Two  instruments  are  always  employed,  which  may  be  exactly 
similar  to  each  other:  (1.)  the  transmitter,  from  the  sending 
station,  applied  to  the  mouth  of  the  sender;  (2.)  the  receiver, 
at  the  distant  station,  applied  to  the  ear  of  the  receiver  of  the 
message ;  (3.)  the  two  instruments  are  connected  by  a  string  or 
by  a  wire. 

The  simplest  form  is  the  "Lover's  Telegraph."  The  instruments 
used  are  two  hollow  cylinders  of  tin.  over  one  end  of  each  is  stretched 
a  piece  of  bladder,  to  serve  as  a  vibrating  membrane,  and  the  two 
membranes  are  connected  by  a  string  or  wire  fastened  to  the  center 
of  each.  When  in  use  (1.)  the  connecting  wire  is  stretched  taut;  (2.) 


435 a  NATURAL  PHILOSOPHY. 

the  sender  speaks  into  the  open  end  of  his  cylinder,  and  thereby  ex- 
cites vibrations  in  the  tense  membrane  of  the  transmitting  instrument ; 
(3.)  these  vibrations  are  transmitted  as  sound  waves  through  the 
wire  to  the  membrane  of  the  receiving  instrument;  (4.)  this  mem- 
brane is  thrown  into  vibrations  exactly  similar  to  those  of  the  trans- 
mitting membrane,  and  (5)  hence  sound  waves  are  excited  in  the 
receiver  which  reproduce  the  speech,  etc.,  of  the  sender  so  as  to  render 
it  audible  to  a  person  whose  ear  is  applied  to  the  open  end  of  the 
receiving  instrument.  This  toy  has  been  so  perfected  that  speech  can 
easily  be  transmitted  over  two  miles  of  straight  wire.  They  are  used 
on  such  short  lines  to  connect  workshops,  etc.,  with  the  salesrooms  in 
manufactories. 

The  Bell  Telephone,  shown  in  Fig.  351,  has  for  its  vibrating  mem- 
brane a  thin  iron  plate  E,  which  is  free  to  move  above,  but  not  quite 
touching,  a  permanent  magnet,  A.  At  the  end  of 
the  magnet  is  a  coil  of  fine  wire,  B,  which  is  con- 
nected with  the  binding  posts,  DD.  One  of  the 
wires  from  D  is  connected  with  the  earth;  the 
other  with  a  distant  station.  No  battery  is  used. 
The  plate,  E,  is  held  in  its  place  by  a  cup-shaped 
cover,  to  which  the  mouth  is  applied  in  sending 
and  the  ear  in  receiving.  The  operation  of  the  in- 
strument is  similar  to  that  of  the  preceding.  (1.) 
A  sound  produced  in  front  of  the  plate,  E,  pro- 
duces waves  of  condensation  and  rarefaction,  which 
cause  movements  in  the  plate  towards  and  from  the 
magnet,  A.  (2.)  Every  such  movement  produces  a 
disturbance  in  the  magnetic  field,  by  means  of 
which  induced  currents  will  be  set  up  in  the  coil,  B  (§  763.)  (3.)  This 
induced  current  is  propagated  through  the  connecting  wire  and  sets 
up  similar  vibrations  in  the  plate  of  the  receiving  instrument.  (4.) 
These  vibrations  excite  in  the  air  sound  waves,  similar  to  those  which 
caused  them,  and  hence  (5)  reproduce  the  original  sounds,  in  pitch, 
ijualitv,  and  even  timbre,  so  faithfully  that  the  characteristic 
f  a  >peaker  are  easily  recognized.  On  long  lines,  however, 
the  sound  transmitted  is  too  feeble  to  be  audible,  and  is,  betides, 
liable  to  become  confused  by  currents  in  adjacent  wires.  To  obvi- 
ate these  difficulties  a  battery  is  used,  and  a  special  transmitter  more 
or  less  resembling  one  of  tin-  two  following  instruments. 

759  a.  The  Microphone  is  an  instrument  capable  of  trans- 
mitting distinctly  very   i'«  1>K-  sounds. 


THE  MICROPHONE. 


4356 


Hughes's  Microphone,  Fig.  351  a,  consists  essentially  of  two  carbon 
sockets  S  and  S',  each  of  which  is  connected  with  one  of  the  wires 
in  a  galvanic  circuit,  and  of  a  carbon  spindle,  C,  placed  vertically 
so  as  to  rest  in  the  lower  socket  and  play  loosely  in  the  upper. 
Now,  if  while  the  current  is  passing,  a  noise  be  made  in  front  of  the 
spindle  C,  it  will  so  jar  the  spindle  as  to  produce  a  greater  or  less 
surface  contact  between  the  ends  of  the  spindle  and  its  sockets.  In 
consequence  of  this,  the  current  transmitted  by  the  battery  will  vary 
in  like  proportion.  These  variations  will  represent  the  sound 
waves,  and  may  be  made  to  reproduce  audible  sounds  if  a  receiving 
instrument  such  as  a  Bell's  telephone  be  interposed  in  the  circuit. 
Xow,  as  the  spindle  is  set  in  motion  by  very  feeble  sounds,  such  as 
the  ticking  of  a  watch,  it  receives  the  original  impulse  strongly, 
and  also  impresses  the  receiving  in- 
strument strongly,  and,  it  is  said,  that 
when  a  powerful  battery  is  used  the 
intensity  of  the  sound  is  increased. 
Fig.  351  b  shows  the  interior  of  the 
Blake  transmitting  telephone,  which 
is  extensively  used  to  send  audible 
messages. 

It  contains  a  diaphragm  which  vi- 
brates  in  answer  to  the  voice  against 
a  small  platinum  disk,  which  is 
thereby  forced  against  a  movable  carbon  cylinder  C.  The  disk  and 
carbon  are  connected  with  a  battery,  and  the  current  will  not  pass 
except  when  these  are  in  contact.  The  amount  of  surface  contact 

between  them  will  of  course  vary 
with  the  condensation  and  rarefac- 
tion of  the  sound  waves,  and  conse- 
quently there  will  be  a  variation  in 
the  resistance  of  the  primary  circuit 
which  may  be  reproduced  as  sound 
waves  in  a  distant  telephone  receiver. 
The  receiving  telephone  is  placed  in 
connection  with  an  induction  coil,  I, 
and  is  worked  by  the  secondary  cur- 
rent. [The  words  primary  and  sec- 
ondary are  defined  in  the  next  article.]  Usually  each  station  has  a 
call,  arranged  on  the  principle  of  fire  alarms.  (§756.) 

There  are  other  forms  of  this  instrument;  some  of  which  have 
rendered  conversation  distinctly  over  250  miles  of  wire. 


FIG.  351  a. 


FIG.  351  6. 


436  NATURAL    PHILOSOPHY. 

ELECTRO-DYNAMIC    INDUCTION. 

760.  The  phenomena  of  current  induction  may  be  shown 
by  the  apparatus  represented  in  Fig.  352.  Let  P  and  I 
be  two  helices  of  insulated  wire,  the  first  connected  with  a 
voltaic  battery,  and  the  other  with  a  galvanometer.  If, 
when  the  current  is  passing  through  P,  it  be  brought  near 


FIG.  352. 


the  helix,  I,  a  momentary  current,  in  the  opposite  direction, 
will  be  induced  in  I,  and  will  be  manifested  by  the  deflec- 
tion of  the  needle  in  the  galvanometer.  The  first  current  is 
called  the  primary, or  inducing,  current,  and  the  other,  the 
secondary,  or  induced,  current. 

A  current  in  the  same  direction  as  the  primary,  is  said 
to  be  direct;  but  if  in  the  opposite  direction,  inverse.  If 
the  two  helices  are  held  in  the  same  relative  position,  the 
induced  current  soon  ceases,  and  the  needle  falls  back  to 
its  old  position.  If  the  primary  coil  is  placed  within  the 
other,  another  momenta! y  inverse  current  is  produced.  This 
will  also  be  the  ca.se,  if  the  intensity  of  the  battery  be  in- 
creased.' If,  however,  the  primary  current  be  weakened, 
the  circuit  broken,  or  the  coil  withdrawn,  a  momentary 
current  will  be  induced,  which  in  i-ach  of  these  cases  will 
be  direct. 


INDUCED    CURRENTS.  437 

Hence,  (1.)  An  inverse  momentary  cut-rent  will  be  induced 
in  u  lu'ujhboriinj  circuit  by  a  primary  current  on  starting,  ap- 
proaching, or  inci-eatfiny  in  intuisity.  (2.)  A  direct  moment- 
ary current  will  be  induced  by  a  primary  current  which 
decreases  in  intensity,  or  ichich  is  removed  or  stopped;  but  (3.) 
A  continuous  and  constant  current  does  not  induce  any  current 
in  a  neighboring  conductor. 

761.  The  induced  currents  are,  therefore,  but  momentary 
in   their  action;  nevertheless,  they  have  all  the   properties 
of  the  primary  currents.     For  instance,  they  may  induce 
other   currents  on   adjacent   circuits,  and  thus  currents  of 
the  third,  fourth,  and  even  of  the  seventh  orders  have  been 
obtained. 

The  direct  induced  and  the  inverse  induced  currents  of  the  same 
order  are  equal  in  quantity,  and,  therefore,  have  the  same  effect  on 
the  galvanometer.  The  direct  induced  current  has  greater  intensity 
than  the  inverse,  and  will,  therefore,  give  rise  to  a  more  powerful 
shock.  The  direct  induced  current  also  magnetizes  to  saturation, 
while  the  inverse  does  not  magnetize. 

The  intensity  of  the  direct  induced  current  is  always  high,  even 
when  excited  by  a  feeble  primary  current,  but  increases  with  the  in- 
tensity of  the  primary.  The  more  rapid  its  action,  the  greater  will 
be  its  intensity,  and  hence  the  more  instantaneously  the  primary  cir- 
cuit is  demagnetized,  the  more  intense  will  be  the  induced  current. 

762.  A   primary   current   may   also   act   inductively   on 
itself,  and  thus  give  rise  to  what  is  called  the  extra  current. 

It  is  this  which  produces  the  spark  on  breaking  the  circuit.  This 
is  particularly  observable  when  the  conducting  wire  has  the  form  of 
a  helix,  because  then  each  spire  acts  inductively  on  the  next  succeed- 
ing one.  The  effect  of  the  extra  current  is  to  prolong  the  duration 
of  the  primary  current  when  the  circuit  is  broken,  and  it,  therefore, 
reduces  the  tension  of  the  induced  currents,  by  retarding  the  sud- 
denness of  the  change. 

763.  Magneto-electrical  induction.  Since  a  helix,  through 
which   a  current   is   passing,    is   essentially   a   magnet,    we 
ought  to   expect  that  a  permanent  magnet  would,  like  it, 
induce  electrical  currents.     In  fact,  if  we  substitute  for  the 


438 


NATURAL    PHILOSOPHY. 


FIG.  353. 


primary  coil,  P,  in  Fig.  352,  a  permanent  magnet,  we  shall 
obtain  almost  identical  effects. 

The  same  phenomenon  may  be  studied  by  placing  a  bar  of  soft  iron 

within  a  helix,  as  shown 
in  Fig.  353,  and  bringing 
above  it  a  strong  perma- 
nent magnet.  The  core  of 
soft  iron  becomes  magnet- 
ized by  induction,  and  in- 
duces an  electrical  current 
in  the  helix,  by  reason  of 
which  the  needle  of  the 
galvanometer  is  deflected 
for  a  moment,  and  then 
returns  to  its  normal  posi- 
tion. On  removing  the 
magnet,  the  needle  is  de- 
flected in  the  opposite  di- 
rection. The  direction  of 
the  currents  depends  upon 
the  pole  of  the  magnet  presented,  and  is  in  accordance  with  Am- 
pere's law,  (738). 

764.  The  magneto- 
electrical  machine  is 
constructed  on  this 
principle.  Fig.  354. 

This  consists  of  a  per- 
manent magnetic  battery, 
A  B,  in  front  of  which  two 
helices  of  fine  copper  wire, 
carefully  insulated,  are 
made  to  revolve  on  an 
axis,/,  by  means  of  a  wheel 
and  winch.  The  cores  of 
the  helices  are  made  of  two 
pieces  of  soft  iron,  joined 
by  a  soft  iron,  ttf.  The 
same  wire  is  coiled  about 
the  two  core-,  hut  in  dif- 
ferent directions,  in  order  that  the  currents  induced  hv  the  opposite 


INDUCTION  COILS.  439 

poles  may  be  in  the  same  direction.  The  two  ends  of  this  wire  ter- 
minate in  two  metallic  plates  insulated  from  the  axis  and  from  each 
other  by  ivory,  and  are  connected  alternately  with  the  springs,  S  S'. 
On  turning  the  wheel,  a  current  of  electricity  is  induced  in  each 
helix,  the  direction  of  which  changes  twice  at  each  revolution. 

765.  This   instrument   is   capable   of  producing  sparks, 
decomposing  water,   and  igniting  wires,  and  of  producing 
other  effects  of  dynamical  electricity.     If  a  break  piece,  not 
shown  in   the  figure,  be   added,  an   extra  current  of  great 
tension  will  be  induced,  which  is  capable  of  producing  very 
powerful  shocks,  if  the  handles,  P  P',  be  grasped  with  the 
hands   slightly   moistened.      With   a   good   apparatus,    the 
muscles  contract  with  such  force  that  they  no  longer  obey 
the  will,  and   the  handles   can  not  be  dropped.     From  its 
convenience  and  neatness,  this  is  a  very  common  apparatus 
for  applying  the  effects  of  induced  currents  in  therapeutical 
operations. 

766.  Other  magneto-electrical  machines  of  remarkable 
power  have  been  constructed  on  the  same  principle. 

They  have  been  used  for  all  the  practical  operations  of  electricity, 
such  as  electroplating,  telegraphing,  and  more  recently  for  the  electric 
light.  The  machines  are  driven  by  a  steam  engine.  Wilde's  machine 
yields  a  light  of  surpassing  brilliancy,  and  evolves  sufficient  heat  to 
melt  iron  rods  15  inches  long  and  \  inch  thick.  The  Gramme  machine, 
and  Brush's  modification  of  it  have  been  successfully  used  to  light  the 
interior  of  large  buildings  and  also  for  street  lamps,  using  some  form 
of  the  electric  arc.  Fig.  332. 

767.  Induction  coils  are  instruments  which  employ  both 
magnetic  and  electric  induction.     One  form   in  which    the 
helices  are  separable  is  shown  in  Fig.  355. 

The  primary  coil,  P,  is,  of  coarse,  insulated  copper  wire,  connected 
by  the  screw  cups,  -f  and  — ,  with  the  battery.  I  is  the  secondary  coil, 
of  very  fine,  insulated  copper  wire,  to  which  handles  may  be  attached. 
M  is  a  bundle  of  iron  wires,  which  are  sufficiently  insulated  from 
each  other  by  the  rust  which  soon  gathers  on  them.  The  primary 
current  is  made  to  open  and  close  by  its  own  action.  This  is  effected 


440  NATURAL   PHILOSOPHY. 

by  a  small  electro-magnet,  B,  the  spring  of  whose  armature  is  made 
to  open  and  close  the  circuit. 

As  soon  as  the  coil  of  B  receives  the  current,  the  armature  is  drawn 
down  and  the  circuit  is  broken.  At  every  interruption  of  the  pri- 
mary current,  the  iron  wires,  M,  become  magnetized  and  demagnetized, 


FIG.  353. 


and  react  upon  the  secondary  coil.  The  intensity  of  the  induced 
currents  is  thereby  much  increased,  and  may  even  become  of  so 
high  tension  as  to  produce  all  the  effects  of  statical  electricity.  The 
form  shown  in  Fig.  355  is  frequently  used  for  giving  shocks,  and  for 
medical  purposes. 

768.  Ruhmkorff's  coil  is  made  on  the  same  principle  as 
that  already  described.  The  utmost  care  is  taken  in  insu- 
lating the  wire  used.  The  secondary  helix  contains  from 
three  to  thirty  miles  of  fine  wire.  To  avoid  the  effect  of  the 
extra  current  of  the  primary  coil,  a  condenser  of  tin  foil  is 
placed  in  the  base  of  the  instrument  and  is  connected  with 
the  interrupter.  This  is  ordinarily  a  ratchet  wheel,  turned 
by  the  hand,  which  breaks  and  closes  the  current  every  time 
its  spring  passes  from  one  tootli  to  another. 

With  three  or  four  Bunsen's .  elements  and  a  lurge  coil 
the  induced  current  becomes  of  ama/ing  tension,  although 
of  inconsiderable  quantity.  Some  of  the  eU'eets  ,,f  die  coil 
follow.-  : 


THERMO-ELECTRICITY.  441 

1.  Physiological.    The  shocks  are  so  violent  as  to  be  dan- 
gerous, and  incautious  experimenters  have  been  prostrated 
by  them. 

2.  Calorific.     Fine  iron  wires  brought  between  the  ends 
of  the  induced  wire  are  melted  and  burned. 

3.  Luminous.     Sparks  have  been  obtained  nineteen  inches 
in  length.     When  the  discharge  is  passed  into  rarefied  air 
or  gases,  the  phenomena  of  auroral  light  is  produced  in  a 
most  beautiful  and  varied  manner. 


FIG.  356. 

These  experiments  are  performed  with  sealed  glass  tubes, 
known  as  Geisler's  tubes,  one  of  wrhich  is  showrn  in  Fig.  356. 
The  color  of  the  light  varies  with  the  vapor  inclosed  in  the 
tube,  and  is  frequently  arranged  in  bands,  giving  the  ap- 
pearance of  stratified  light.  To  produce  these  effects  with 
the  primary  current  would  require  a  battery  of  over  fifty 
elements. 

4.  Leyden  jars  may  be  charged  and  discharged  by  means 
of  the  coil  with  an  almost  continuous  spark,  of  great  bril- 
liancy and  accompanied  by  an  almost  deafening  sound. 

These,  as  well  as  the  mechanical  and  chemical  effects  of 
the  coil,  are  similar  to  those  produced  by  statical  electricity. 

THERMO-ELECTRICITY. 

769.  If  any  two  metals  are  soldered  together  and  heated 
at  their  junction,  an  electrical  current  is  evolved  which  is 
capable  of  deflecting  the  needle  of  the  galvanometer.  On 


442 


NATURAL  PHILOSOPHY. 


the  other  hand,  if  their  junction  be  cooled,  the  needle  will 
be  deflected  in  the  opposite  direction.     These  currents  are 

called  thermo-electric  currents, 
but  they  differ  in  no  respect 
.     from  those  already  studied. 

770.  The  direction  of  the 
current  within  the  pair  will 
depend  on  the  metals  which 
are  associated  together.  The 
following  thermo-electric  se- 
ries is  so  arranged  that  if  any 
two  of  the  substances  named  are  soldered  together,  and 
heated  at  the  soldering,  the  current  will  pass  from  the  first 
named  to  that  succeeding  it. 


FIG.  357. 


t-t    3 

~    -    •- 

ft  -~     « 


c  •£    § 
"    c  ^ 


771.  The  most  efficient  electro-thermal  couple  is  said  to 
be  formed  of  artificial  sulphide  of  copper  and  metallic 
copper.  Fig.  357.  The  usual  combination  is  bars  of  anti- 
mony and  bismuth. 

Fig.  358  shows  a  section  of  a  thermal  battery  made  up  of  these 
metals.  The  greater  the  number  of  pairs,  the  greater  will  be  the 
force  of  the  current.  Although  the  electro-motive 
force  of  a  thermal  battery  is  always  low,  it  may 
be  used  to  attain  the  same  results  as  the  voltaic 
battery. 

Since  in  combining  the  pairs  it  is  necessary  to 
join  both  ends  of  all  except  the  outer  bars,  the 
effect  of  the  current  will  be  due  to  the  difference 
in  the  temperature  of  the  two  ends. 


Fio.  358. 


This  fact  is  utilized  in  the  thermo-multiplier  shown  at  T 
in  Fig.  359.  This  consist <  <>\'  thirty  pairs  of  bismuth  and 
;mtimony,  inclosed  in  a  non-conducting  frame,  and  con- 


ANIMAL   ELECTRICITY. 


443 


nected  with  a  galvanometer  which  has  only  a  few  turns  of 
tolerably  thick  wire.     This  apparatus  is  so  sensitive  that 


FIG.  359. 

even  the  radiant  heat  emitted  by  insects  may  be  estimated 
by  it.  It  is  therefore  used  in  all  delicate  investigations  on 
the  subject  of  radiant  heat. 

ANIMAL    ELECTRICITY. 

772.  We   have    already    seen   that   electricity   produces 
peculiar  phenomena  in  living  animals,  and  that  one  of  the 
most  sensitive  galvanoscopes  may  be  had  in  the  legs  of  a 
recently  killed   frog.     Matteuci  has  reversed  this  last  ex- 
periment, and  has  succeeded  in  evolving  a  current  by  means 
of  a  battery  formed  of  the  muscles  of  frogs. 

773.  Several  species  of  fish  have  the  power  of  giving, 
when  touched,  shocks  like  those  of  the  Leyden  jar.    Among 
these  are  the  torpedo,  the  gymnotus,  and  the  silurus.    Each 
of  these  fish  has  special  organs  for  the  production  of  elec- 
tricity.    This  electrical  apparatus  is   under  the  control  of 
the   animal,    and   may  be   made   to   serve   as  a  means   of 
offense  and  defense. 

It  is  thought  by  some  philosophers  that  electrical  currents  are 
evolved  and  consumed  in  all  animals  during  the  various  vital  proc- 
esses, like  secretion,  digestion,  and  the  like.  None  of  these  theories 
are  sufficiently  well  established  to  be  introduced  here. 


444  NATURAL   PHILOSOPHY. 

774.  Becapitulation. 

I.  The  science  of  electricity  includes  the  phenomena  of 

1.  Electricity  that  may  be  insulated Statical. 

2.  Electricity    continually    discharged    in 

currents Dynamical. 

Dynamical  electricity  investigates  the  phenomena 

I.  Within  the  path  of  the  current : 

1.  Due  to  chemical  action Galvanism. 

2.  Due  to  heat Thermo-electricity. 

3.  Due  to  vital  action Animal  electricity. 

4.  Due  to  Amperean  currents Magnetism. 

II.  External  to  the  path  of  the  current : 

1.  Inducing  magnetism  in  iron  and  steel...Electro-magnetism. 

2.  Inducing  currents  in  adjacent  circuits. ...Electro-dynamics. 

III.  Of    currents    induced    by    permanent 

magnets Magneto-electricity. 

Induced  currents  are  applied 

1.  For  physiological  and  therapeutical  purposes. 

2.  For  evolving  light  and  heat  of  great  intensity. 

3.  For  effecting  chemical  changes. 

4.  For  making  temporary  and  permanent  magnets,  which  are 

employed  to  produce  mechanical  action  in  engines,  tele- 
graphs, clocks,  etc. 


PROBLEMS. 


THE  object  sought  in  these  problems  is  rather  to  enforce 
the  principles  of  Physics  than  to  afford  practice  in  arith- 
metic. They  are  therefore  as  easy  as  circumstances  will 
permit.  In  their  solution  it  will  not  be  necessary,  as  a  gen- 
eral thing,  to  employ  more  than  two  places  of  decimals. 
The  student  will  understand  that  they  are  to  be  solved 
only  in  view  of  the  principle  involved,  and  that  circum- 
stances modifying  the  application  of  the  theory  in  actual 
practice  are  excluded.  The  solutions  should  be  preserved 
for  reference  and  comparison. 

USEFUL    FACTORS. 

77  =  3.1416 7T2      =      9.87. 

Circumference  of  a  circle 2?rr    =    -rrd    =  3.1416d. 

Area  of  a  circle *r*  =  frd2  =    .7854d2. 

Surface  of  a  sphere ±*rz  =   vd2  =  3.1416d2 . 

Volume  of  a  sphere f*r3  =  frd3  =0.5236d3. 

SOMATOLOGY. 

Art.  17.  1.  How  many  metres  in  an  English  mile?  How  many 
mile?  in  a  kilometre?  What  part  of  an  inch  is  a  millimetre?  How 
many  inches  in  776  millimetres? 

2.  The  radius  of  the  earth  is  3963  miles ;  find  its  circumference. 

3.  The  distance  of  the  earth  from  the  sun  is  91430000  miles ;  find 
the  circumference  of  its  orbit,  supposing  it  to  be  an  exact  circle. 

4.  If  the  radii  of  two  circles  are  given,  what  is  the  ratio  between 
their  circumferences?     Between  their  areas? 

5.  Find  the  area  of  a  circle  whose  radius  is  1  inch;  10  inches;  T\y 
of  an  inch. 

(445) 


446  NATURAL   PHILOSOPHY. 

6.  How  much  more  water  will  flow  through  a  2  inch  pipe  than 
through  a  1  inch  pipe? 

7.  What  is  the  ratio  between  the  surfaces  of  two  spheres  whose 
radii  are  given?    Between  their  volumes? 

8.  Find  the  spherical  surface  of  an  inch  ball ;  a  10  inch  ball ;  j-s 
of  an  inch  ball. 

9.  Find  the  volume  of  an  inch  ball ;   a  10  inch  ball ;   a  TV  of  an 
inch  ball. 

10.  Find  the  cubic  inches  in  a  pint.     Find  the  litres  in  a  gallon. 
How  many  gallons  in  a  cubic  foot?    How  many  cubic  feet  in  10 
gallons?     How  many  litres  in  a  cubic  foot? 

Art.  19.  11.  How  many  grammes  in  a  pound? 

12.  What  is  the  volume  of  a  pound  of  water?  What  is  the  weight 
of  a  pint  of  water  ?  What  is  the  weight  of  a  cubic  inch  of  mercury  ? 
How  many  grains  in  a  cubic  foot  of  hydrogen  ?  What  is  the  volume 
of  a  pound  of  hydrogen? 

Art,  24.  13.  Calculate,  from  Example  2,  the  velocity  per  minute 
of  a  point  on  the  equator. 

14.  Calculate,  from  Example  3,  the  velocity  per  minute  of  the 
earth  in  its  orbit. 

15.  Find    the   time    required    for  electricity    to    pass   around    the 
equator.     For  sound  to  traverse  the  same  distance. 

16.  Find   the  space  that  light  will  traverse  in  8  minutes  and  13 
seconds.     How  far  will  a  rifle  ball  go  in  3  seconds? 

17.  How  long  would  it  take  a  railway  train  to  reach  the  sun? 

Art.  29.  18.  An  ounce  of  water  contains  360  drops :  if  a  grain  of 
nitrate  of  copper  be  dissolved  in  a  gallon  of  water,  how  much  nitrate 
of  copper  will  there  be  in  a  single  drop  ? 

Art.  30.  19.  Suppose  a  grain  of  water  be  blown  into  a  soap  bubble 
10  inches  in  diameter,  what  will  be  the  weight  of  the  water  in  each 
square  inch  of  the  film? 

Art.  38.  20.  Find  the  weight  of  a  cubic  foot  of  cork ;  of  ice ;  of  a 
ball  of  silver  10  inches  in  diameter.  Of  a  pint  of  alcohol. 

21.  Find  the  weight  of  a  gallon  of  ammonia  in  both  the  liquid  and 
:i-  rit'orm  states. 

22.  How  many  times  heavier  is  a  cubic  inch  of  platinum  than  i.f 
hydrogen  ? 


PROBLEMS   ON  MECHANICS.  447 

Art.  42.  23.  How  deep  must  water  be  at  39°.2F.  to  equal  the 
pressure  of  one  atmosphere  ?  at  62°  ? 

24.  What  is  the  pressure  in  pounds  indicated  by  a  column  of  mer- 
cury at  62°  F.  and  eighteen  inches  high  ? 

25.  How  many  feet  of  air  are  required  to  produce  the  same  press- 
ure as  30  inches  of  mercury  at  32°  F. 

26.  Suppose  a  boy  has  a  surface  of  8|  square  feet,  what  is  the 
atmospheric  pressure  he  sustains? 

Art.  62.  27.  How  much  will  a  rod  of  steel,  1  inch  in  section  and 
10  feet  long,  be  stretched  by  a  weight  of  100000  pounds? 

28.  How  much  force  is  required  to  crush  a  cubic  foot  of  oak  ?    Of 
cast  iron? 

29.  How  much  force  is  required  to  overcome  the  tenacity  of  a 
steel  wire  y1^  of  an  inch  in  diameter? 

Art.  74.  30.  What  is  the  weight  of  the  finest  platinum  wire  a 
mile  long  ?  What  is  the  weight  of  a  square  inch  of  finest  gold  leaf? 

Art.  93.  31.  How  many  gallons  of  ammonia  may  be  absorbed  by 
a  pint  of  water  ?  What  will  the  solution  weigh  ? 

Art.  95.  32.  How  many  gallons  of  ammonia  may  be  absorbed  by 
a  cubic  foot  of  charcoal? 

33.  What  weight  of  carbonic  acid  may  be  absorbed  by  a  cubic  foot 
of  charcoal  ? 

MECHANICS. 

Art.  114.  34.  Find  the  momentum  of  a  glacier  300  feet  high,  5 
miles  long,  and  1  mile  wide,  moving  at  the  rate  of  1  mile  a  month. 

35.  Find  the  momentum  of  a  locomotive  weighing  25  tons,  and 
having  a  velocity  of  30  miles  per  hour. 

36.  Find  the  velocity  of  a  cannon  ball  weighing  60  pounds,  and 
having  a  momentum  of  30000  pounds.     Find  the  weight  of  a  ball 
that  has  the  same  momentum  and  a  velocity  of  1200  feet  per  second. 

Art.  120.  37.  Two  forces,  A  and  B,  act  on  the  same  point;  A  with 
a  force  of  90  pounds,  B  with  120;  what  will  be  their  resultant  if 
they  lie  in  the  same  direction?  If  in  opposite  directions?  If  at 
right  angles  to  each  other? 

Art.  123.  38.  The  resultant  of  two  forces  acting  at  right  angles  is 
10 ;  one  of  the  forces  is  8 ;  what  is  the  other  ? 
N.  P.  29. 


448  NATURAL   PHILOSOPHY. 

Art.  125.  39.  Suppose  two  equal  forces  act  at  an  angle  of  60  de- 
grees; what  will  be  the  direction  and  force  of  their  resultant?  If  one 
force  be  double  that  of  the  other?  Apply  the  method  by  construction. 

Art.  128.  40.  If  two  inelastic  bodies— A  having  a  weight  of  3 
pounds  and  a  velocity  of  5  feet  per  second,  B  having  a  weight  of  4 
pounds  and  a  velocity  of  3  feet  per  second— collide  from  opposite  di- 
rections, what  will  be  the  resulting  momentum,  velocity,  and  direction  ? 
If  they  move  in  the  same  direction,  and  A  strikes  against  B,  what 
will  be  the  resulting  momentum  and  velocity  ? 

Art.  129.  41.  In  the  last  example,  what  would  have  been  the 
result  if  the  bodies  had  been  perfectly  elastic  ? 

Art.  134.  42.  Calculate  the  striking  force  in  examples  34  and  35. 

43.  If  light  were  matter,  and  one-millionth  part  of  a  grain  entered 
the  eye  in  a  second,  what  would  be  its  striking  force  as  compared  with 
an  ounce  rifle  ball  with  a  velocity  of  1200  feet  per  second? 

44.  How  fast  must  a  battering  ram  weighing  3  tons  be  propelled  in 
order  to  have  the  same  striking  force  as  a  30  pound  cannon  ball  with 
a  velocity  of  1200  feet  per  second?    With  equal  vis  viva,  how  would 
their  momenta  compare? 

Art.  143.  45.  If  two  cannon  balls,  weighing  respectively  30  and 
80  pounds,  be  connected  by  a  rigid  bar,  where  will  the  common 
center  of  gravity  be? 

46.  If  the  mass  of  the  moon  is  ?T  that  of  the  earth,  where  is  their 
common  center  of  gravity  ? 

Art.  154.  47.  What  is  the  work,  expressed  in  foot-pounds,  that  is 
required  to  raise  193  pounds  4  feet  high?  To  raise  10000  gallons 
of  water  from  the  bottom  of  a  mine  600  feet  deep? 

Art.  155.  48.  How  many  horse  powers  are  required  to  fill  every 
day  a  reservoir,  having  a  capacity  of  a  million  cubic  feet,  with  water 
from  a  lake  400  feet  below  the  reservoir? 

Art.  157.  49.  Suppose  a  power  of  50  pounds  moves  throuirh  a  ver- 
tical distance  of  10  feet,  how  high  can  it  lift  a  load  of  250  pounds? 
How  great  a  load  can  it  lift  100  fret  high?  In  each  case,  what  will  be 
the  relative  velocities  «.f  the  power  :md  the  load? 

Art.  162.  ."iO.  A  power  of  7")  pound-  i-  applied  at  one  end  of  a 
lever  12  feet  long,  to  move  a  load  at  the  other  end;  what  will  he  the 
load  when  the  fulcrum  i-  at  the  center  <>\'  the  lever'/  When  tin-  ful- 
crum is  3  feet  from  the  load?  1  loot  from  the  load? 


PROBLEMS   ON  MECHANICS.  449 

51.  When  the  same  bar  is  employed  as  a  lever  of  the  second  kind, 
what  will  be  the  load  when  it  is  sustained  at  the  center?  At  3  feet 
from  the  fulcrum  ?  At  one  foot  ? 

•VJ.  If,  with  the  same  bar,  the  load  and  the  fulcrum  be  placed  at  the 
ends,  and  the  power  applied  between  them,  what  will  be  the  load  when 
the  power  is  at  the  center?  At  3  feet  from  the  fulcrum ?  At  1  foot? 

53.  If,  with  the  same  bar,  a  power  of  30  pounds  balances  a  load  of 
180  pounds,  how  far  from  the  load  will  the  fulcrum  be  when  it  is  used 
as  a  lever  of  the  first  kind?  As  a  lever  of  the  second  kind ? 

Art.  166.  54.  If  A  and  B  carry  between  them,  on  a  pole  9  feet 
long,  a  load  of  150  pounds,  how  much  will  A  bear  when  the  load  is 
3  feet  from  him  ?  6  feet  ? 

Art.  167.  55.  In  the  compound  lever,  shown  in  Fig.  47,  A  F  is  6 
feet  long,  A'  B'  4  feet,  A"  F"  5  feet,  and  the  distances,  F  B,  Fx  B', 
F"  B/x,  each  1  foot ;  what  is  the  relation  between  the  power  and  the 
load?  What  load  may  be  sustained  by  a  power  of  60  pounds? 

How  far  from  B  must  a  power  of  10  pounds  be  placed  to  balance 
a  load  of  300  pounds  at  L. 

Art.  171.  56.  In  a  false  balance,  a  bundle  weighs  16  pounds  in  one 
scale  pan  and  9  pounds  in  the  other ;  what  is  the  true  weight  ?  What 
is  the  relative  length  of  the  arms  ?  Prove  the  answers  obtained. 

Art.  175.  57.  In  a  wheel  and  axle,  the  radius  of  the  wheel  is  10 
feet  and  that  of  the  axle  6  inches;  required,  the  load  that  may  be 
sustained  by  a  power  of  1  pound  ?  By  100  pounds  ? 

Art.  176.  58.  With  the  same  machine,  what  will  be  the  length  of 
the  rope  unwound  from  the  wheel,  when  the  load  has  been  lifted  10 
feet? 

Art.  177.  59.  A  capstan  has  an  axle  1  foot  in  diameter,  and  is  fur- 
nished with  5  handspikes,  each  6  feet  long;  how  much  power  must  be 
applied  at  each  handspike  to  lift  an  anchor  weighing  4000  pounds? 

Art.  178.  60.  In  a  differential  wheel  and  axle,  the  two  parts  of  the 
axle  are  respectively  8  and  10  inches  in  diameter;  what  is  the  load 
that  may  be  lifted  by  this  machine  by  a  power  of  100  pounds,  ap- 
plied at  a  winch  of  2  feet  radius? 

Art.  179.  61.  In  a  train  of  three  wheels,  the  number  of  teeth  in 
each  wheel  is  64,  the  number  of  leaves  on  each  pinion  16;  when  a 
power  of  10  pounds  is  applied  at  the  circumference  of  the  first  wheel, 
what  load  will  be  sustained  at  the  third  pinion?  How  many  times 
must  the  first  wheel  revolve,  in  order  that  the  third  pinion  may  be 
turned  around  once? 


450  NATURAL   PHILOSOPHY. 

62.  In  Fig.  176,  the  cord,  D,  passes  from  the  wheel,  A,  5  feet  in 
diameter,  to  the  axle  of  the  second  wheel,  B,  2  inches  in  diameter ; 
how  many  times  faster  will  B  revolve  than  A?  B  has  100  teeth  which 
strike  against  a  card,  E;  how  many  teeth  will  strike  the  card  when  A 
has  revolved  once? 

Art.  185.  63.  In  a  system  of  2  movable  pulleys,  with  a  continuous 
cord,  the  power  is  100  pounds ;  required  the  load. 

64.  What  power  will  be  required  to  raise  2000  pounds  with  a  sys- 
tem of  4  movable  pulleys? 

Art.  187.  65.  In  the  Spanish  burton,  shown  in  Fig.  64,  what  power 
will  be  required  to  lift  one  ton? 

Art.  189.  66.  On  a  road  rising  1  foot  in  25,  what  power  will  be  re- 
quired to  sustain  a  wagon  weighing  1000  pounds? 

67.  A  plank  16  feet  long  extends  from  the  ground  to  a  wagon  4  feet 
high  ;  required  the  power  necessary  to  roll  a  cask  weighing  500  pounds 
into  the  wagon.     What  would  be  the  power  required  if  applied  par- 
allel with  the  ground  ? 

68.  Apply  the  method  by  construction  to  find  the  power  required 
when  applied  at  an  angle  of  40°. 

Art.  198.  69.  In  a  book-binder's  press  the  lever  is  6  feet  long,  and 
the  threads  of  the  screw  0.5  inch  apart ;  what  pressure  may  be  applied 
by  a  power  of  100  pounds? 

70.  In  the  differential  screw,  the  threads  of  the  two  screws  are  re- 
spectively \  and  £  of  an  inch  apart;  through  what  space  will  the  plate 
move  when  the  lever  is  turned  90°? 

Art.  201.  71.  In  the  crane,  Fig.  75,  the  axle  at  G  is  6  inches  in 
diameter,  and  the  winch  3  feet  in  radius,  with  one  movable  pulley ; 
what  will  be  the  relation  between  the  power  and  the  load?  The 
wheel  and  axle  remaining  the  same,  what  advantage  may  be  gained 
by  the  use  of  a  system  containing  4  movable  pulleys? 

Art.  202.  72.  In  Fig.  76,  suppose  the  muscle  to  be  applied  1  inch 
from  the  joint,  and  the  length  of  the  fore-arm  to  be  15  inches;  required 
the  power  necessary  to  raise  a  weight  of  10  pounds. 

Art.  207.  73.  Suppose  an  oak  block  weighing  100  pounds  rest 
upon  an  oak  plank,  with  their  fibers  parallel.  What  will  be  the 
force  required  (1.)  to  start  and  (2.)  to  keep  the  block  in  motion,  if 
no  unguents  are  used? 


PROBLEMS   ON  MECHANICS.  451 

Art.  208.  74.  A  wagon  weighs  2000  pounds.  What  will  be  the 
power  required  to  draw  it  over  a  well  paved,  level  road?  Over  a 
dry  highway?  Suppose  the  road  to  rise  1  foot  in  30,  what  will  be 
the  power  necessary  in  each  case? 

Art.  210.  75.  What  force  will  be  required  to  draw  a  scow  with 
blunt  bow,  having  a  submerged  area  of  8  feet  broad  and  2  deep, 
through  water  at  the  rate  of  1  foot  per  second?  Of  1  foot  per 

minute? 

Art.  211.  76.  In  the  problems  already  detailed  for  machines, 
what  allowance  must  be  made  for  friction  ? 

Art.  219.  77.  A  body  falls  freely  through  the  air.  What  will  be 
the  space  described  in  the  fifth  second?  The  velocity  at  the  end  of 
the  sixth  second  ?  The  total  space  described  in  8  seconds  ? 

Art.  220.  78.  What  will  be  the  velocity  attained  by  a  body  falling 
from  a  vertical  cliff  784  feet  high?  In  what  time  will  it  fall? 

Art.  221.  79.  Suppose  a  smooth  plane  to  extend  10000  feet  up  a 
mountain  side,  with  an  inclination  of  1  foot  in  10,  and  that  a  smooth 
ball  rolls  from  the  top  to  the  bottom.  What  will  be  the  time  required 
for  the  descent?  What  will  be  the  velocity  attained? 

Art.  223.  80.  In  the  case  supposed,  what  will  be  the  space  passed 
over  in  5  seconds  if  the  ball  is  started  with  a  velocity  of  100  feet  per 
second  ? 

Art.  224.  81.  With  what  velocity  must  a  ball  be  thrown  to  strike 
the  top  of  a  flag-staff  257.32  feet  high  ?  What  will  be  the  time  re- 
quired for  its  flight? 

Art.  226.  82.  Suppose  a  rifle  ball  is  shot  horizontally,  with  a 
velocity  of  1200  feet  per  second.  What  will  be  its  range  if  shot  from 
a  rest  4  feet  high?  From  a  rest  64  feet  high? 

Art.  229.  83.  Suppose  the  radius  of  the  moon  were  the  same  as 
that  of  the  earth,  what  would  be  the  weight  of  a  terrestrial  pound 
when  taken  to  its  surface?  Assuming  the  lunar  radius  to  be  \  that 
of  the  earth,  what  would  be  the  weight  of  a  terrestrial  pound  taken 
to  the  surface  of  the  moon  if  its  mass  were  the  same  as  that  of  the 
earth  ? 

84.  If  the  moon's  mass  be  assumed  as  .0128  and  its  radius  as  .24, 
what  would  be  the  weight  of  a  terrestrial  pound  taken  to  its  surface? 


452  NATURAL   PHILOSOPHY. 

85.  If  the  mass  of  the  sun  be  314760  and  its  radius  110  times  that 
of  the  earth,  what  would  be  the  weight  of  a  terrestrial  pound  on  its 
surface?  What  would  be  the  space  passed  over  in  the  first  second  by 
a  falling  body  ? 

Art.  230,  86.  If  a  body  were  dropped  from  a  distance  of  12000 
miles  from  the  earth's  center,  how  far  would  it  fall  in  10  seconds? 

Art.  232.  87.  What  would  be  the  weight  of  a  cubic  foot  of  iron 
500  miles  below  the  surface  of  the  earth  ? 

Art.  238.  88.  What  is  the  length  of  a  pendulum  at  New  York 
that  vibrates  in  £  of  a  second?  In  3  seconds?  What  is  the  ratio 
between  the  lengths  of  these  two  pendulums?  How  long  should  a 
pendulum  be  to  vibrate  100000  times  in  a  day  ? 

Art.  239.  89.  Find  the  increment  of  velocity  due  to  gravity  at 
Spitzbergen  from  the  length  of  the  seconds  pendulum  —  39.21614 
inches. 

Art.  257.  90.  What  will  be  the  centrifugal  force  of  a  wheel  10 
feet  in  radius,  whose  weight  may  be  considered  as  concentrated  in  a 
rim  weighing  1000  pounds,  when  the  wheel  makes  1  revolution  in  a 
second  ?  5  revolutions  in  a  second  ? 

91.  With  what  speed  must  a  pail  of  water  be  whirled  over  the 
head  to  prevent  the  water  from  falling  out,  granting  that  the  radius 
of  the  circle  in  which  the  pail  revolves  is  3  feet? 

HYDROSTATICS. 

Art.  274.  92.  Find  the  pressure  on  the  bottom  of  a  reservoir  120 
feet  long  and  40  feet  wide,  when  the  water  is  at  a  depth  of  10  feet. 

93.  A  pipe  leading  from  the  reservoir  descends  100  feet  into  a 
valley.  What  is  the  pressure  on  each  square  foot  at  the  bottom  of  the 
valley? 

Art.  275.  94.  What  is  the  pressure  on  each  side  of  the  reservoir? 
What  is  the  total  pressure  at  the  sides  and  the  bottom  ?  What  is  the 
weight  of  the  water  contained  in  the  reservoir? 

Art.  276.  95.  What  is  the  pressure  on  a  cubic  foot  of  iron  sunk 
in  water  to  the  depth  of  a  mile? 

Art.  277.  96.  In  Pascal's  experiment,  suppose  the  pipe  to  have 
had  an  area  of  5  square  inches,  what  would  have  been  the  weight  of 
water  in  the  tube?  What  would  have  been  the  pressure  on  each 
square  inch  ? 


PROBLEMS    ON  HYDROSTATICS.  453 

Art.  278.  97.  If  the  upper  board  of  the  hydrostatic  bellows  has 
an  area  of  100  square  inches,  and  a  boy  standing  upon  it  raises  water 
in  the  pipe  to  the  height  of  30  inches,  what  is  the  weight  of  the  boy? 

Art.  280.  98.  In  Bramah's  press,  suppose  a  power  of  1000  pounds 
to  be  applied  at  one  end  of  a  lever  of  the  second  class  10  feet  long, 
whose  weight  is  3  inches  from  the  other  end,  and  suppose  the  larger 
cylinder  to  have  1000  times  the  area  of  the  smaller:  what  will  be  the 
pressure  on  the  ram? 

99.  If  the  larger  cylinder  have  an  area  of  200  inches,  what  will  be 
the  pressure  on  each  square  inch?  How  high  a  column  of  water 
would  this  pressure  support? 

Art.  284.  100.  If  the  discharge  pipe  of  an  Artesian  well  is  200 
feet  above  the  surface,  what  is  the  least  elevation  possible  for  its 
distant  source? 

Art.  286.  101.  At  what  distance  can  a  mountain  5  miles  high  be 
seen  from  the  sea-level  ? 

Art.  289.  102.  What  will  be  the  buoyant  effort  of  water  on  a 
cubic  foot  of  iron  immersed  in  it?  How  much  weight  will  a  cubic  foot 
of  iron  lose  when  immersed  in  water?  Of  lead? 

Art.  291.  103.  What  is  the  volume  of  water  displaced  by  a  cubic 
foot  of  cork?  Of  ice? 

Art.  293.  104.  How  many  cubic  feet  of  water  must  an  iron  boat 
weighing  480  pounds  displace  in  order  that  it  may  float?  If  it  dis- 
places twice  this  volume,  how  many  pounds  will  it  carry  ? 

Art.  301.  105.  From  the  table  on  page  16  calculate  the  specific 
gravity  of  iron :  of  copper.  From  the  tables  on  pages  24  and  25  find 
the  weight  of  a  cubic  inch  of  oak :  of  glass :  of  lead. 

106.  How  much  weight  will  a  pound  of  iron  lose  when  immersed 
in  water?     How  much  will  a  pound  of  lead  lose? 

107.  Find  the  volume  of  a  pound  of  lead.     Of  a  pound  of  iron. 

108.  If  a  pound  of  lead  be  in  a  cubical  shape,  what  will  be  the 
length  of  each  side? 

Art.  302.  109.  A  mass  of  iron  pyrites  weighs  6  ounces  in  air  and 
4.8  ounces  in  water.  What  is  its  specific  gravity? 

Art  303.  110.  The  same  mass  attached  to  an  ounce  of  cork  weighs 
in  water  4.7  ounces.  What  is  the  specific  gravity  of  the  cork  ? 


454  NATURAL   PHILOSOPHY. 

Art.  304.  111.  480  grains  of  carbonate  of  potassa  weighs  in  alcohol 
270  grains.  The  specific  gravity  of  the  alcohol  being  .85,  required  the 
specific  gravity  of  the  carbonate  of  potassa. 

Art.  305.  112.  A  small  flask  contains  900  grains  of  water,  800 
grains  of  alcohol,  or  1350  grains  of  sulphuric  acid.  Required  the 
specific  gravity  of  the  alcohol  and  sulphuric  acid. 

113.  A  boy's  marble  weighs  in  air  450  grains,  in  water  300  grains, 
in  naphtha  350  grains.  Required  the  specific  gravity  of  the  naphtha. 

Art.  306.  114.  If  1500  grains  are  required  to  sink  a  Nicholson's 
hydrometer  to  the  mark  on  the  stem,  what  will  be  the  specific  gravity 
of  a  solid  that  requires  1000  grains  to  be  added  to  the  pan  when  the 
body  is  on  the  scale  pan,  and  1100  grains  when  the  body  is  in  the 
basket  ? 

Art.  308.  115.  What  is  the  specific  gravity  of  a  liquid  correspond- 
ing to  30°  Beaume?  For  heavier  liquids?  For  lighter  liquids? 

Art.  309.  116.  A  flask  full  of  air  weighs  131  grains ;  when  full 
of  carbonic  acid,  146  grains ;  the  flask  weighs  100  grains.  What  is 
the  specific  gravity  of  the  carbonic  acid  ? 

Art.  311.  117.  A  nugget  of  quartz  and  gold  weighs  in  air  10 
ounces,  and  loses  2  ounces  in  water ;  the  specific  gravity  of  the  quartz 
being  2.5.  How  much  gold  does  the  nugget  contain  ? 

HYDRODYNAMICS. 

Art.  314.  118.  With  what  velocity  will  water  flow  from  an  orifice 
25  feet  below  the  surface?  What  will  be  the  relative  velocities  of  two 
streams  respectively  9  and  16  feet  below  the  surface? 

Art.  315.  119.  What  will  be  the  range  of  a  stream  escaping  from 
the  center  of  a  reservoir  72  feet  high  ? 

Art.  316.  120.  What  will  be  the  theoretical  volume  discharged 
per  minute  from  each  orifice,  in  the  above  examples,  supposing  the 
head  to  be  constant,  and  the  diameter  of  the  stream  1  inch  ? 

Art.  318.  121.  What  will  be  the  volume  if  allowance  is  made  for 
the  vena  contracts  without  adjutage?  What  with  a  good  adjutage? 

Art.  322.  122.  If  the  flow  of  the  Mississippi  were  not  retarded  by 
the  shape  of  its  bed,  etc.,  what  would  be  its  velocity  at  its  mouth, 
which  is  1572  feet  below  its  source? 


PROBLEMS   ON  PNEUMATICS.  455 

Art.  323.  123.  What  i.s  the  gross  power  of  a  stream  flowing 
through  a  weir  having  a  section  of  4  square  feet  and  a  fall  of  9  feet  ? 

Art.  326.  124.  What  will  be  the  eflective  power  of  the  same 
stream  when  applied  to  an  overshot  wheel  ?  To  a  turbine  ? 

PNEUMATICS. 

Art.  338.  125.  How  high  must  a  barometer  tube  be  if  filled  with 
sulphuric  acid,  having  a  density  of  1.84? 

Art.  339.  126.  How  heavy  a  brick  may  be  raised  by  a  boy's 
sucker,  whose  effective  diameter  is  2  inches  ? 

Art.  340-  127.  What  is  the  pressure  on  each  square  inch  required 
to  condense  air  to  TV  of  its  original  volume  ? 

Art.  344.  128.  If  an  air  pump  exhausts  y^  of  the  air  from  a 
receiver  at  each  stroke,  what  will  be  the  tension  of  the  air  remain- 
ing at  the  fifth  stroke? 

Art  345.  129.  What  will  be  the  pressure  on  a  pair  of  Magdeburg 
hemispheres  2  inches  in  diameter  when  the  gauge  of  the  pump  stands 
at  24  inches? 

130.  How  heavy  a  load  may  be  raised  by  a  weight  lifter  whose 
diameter  is  3  inches? 

131.  How  much  weight  will  be  gained  respectively  by  10  pounds  of 
lead  and  of  cork  when  transferred  to  a  vacuum  ? 

132.  What  is  the  ascensional  power  of  a  spherical  balloon  100  feet 
in  diameter,  and  filled  with  coal  gas  of  a  specific  gravity  of  0.5? 

Art.  346.  133.  Tf  the  cylinder  of  a  condensing  pump  is  Ta7  the 
volume  of  its  receiver,  what  will  be  the  tension  of  the  condensed  air 
after  50  strokes  of  the  piston? 

Art.  351.  134.  What  will  be  the  variations  in  atmospheric  pressure 
due  to  a  range  of  3  inches  in  the  barometer? 

Art.  354.  135.  What  will  be  the  difference  in  pressure  on  the  body 
of  an  average  sized  man  ? 

Art.  355.  136.  On  the  same  man,  when  he  has  descended  in  a 
diving  bell  17  feet  ? 

Art.  359.  137.  Wrhat  is  the  pressure  required  to  force  a  stream  of 
water  75  feet  high  ? 

Art.  361.  138.  What  is  the  greatest  vertical  height  possible  for  a 
siphon  used  for  transferring  alcohol? 


456  NATURAL   PHILOSOPHY. 

ACOUSTICS. 

Art.  397.  139.  What  is  the  relative  intensity  of  two  sounds  from 
the  same  source  heard  at  the  distances  of  10  and  250  feet? 

Art.  406.  140.  With  air  at  32°  F.,  how  long  will  it  take  sound  to 
travel  1  mile?  How  long  with  air  at  90°  F.? 

141.  A  stone  dropped  into  a  deep  well  returns  the  sound  in  3  sec- 
onds ;  required  the  depth  of  the  well. 

Art.  409.  142.  An  iron  gas  pipe  is  5  miles  long;  required  the 
time  for  a  blow  struck  at  one  end  to  be  heard  at  the  other,  through 
the  iron  and  through  the  air.  (The  velocity  of  sound  in  iron  may  be 
taken  as  the  same  as  in  steel.) 

Art.  421.  143.  A  string  which  sounds  Cl  is  2  feet  long ;  what  must 
be  the  length  of  the  same  string  to  sound  C_l}  A2,  G3  ? 

144.  If  the  same  string  is  made  8  inches  long,  what  will   be  the 
sound  that  may  be  emitted  by  it?    With  what  relative  force  must  the 
original  string  be  stretched  to  sound  G2  ? 

145.  Suppose  a  string  of  the  same  material,  but  of  quadruple  the 
relative  weight,  sounds  C^  what  is  its  length  ? 

Art.  422.  146.  What  is  the  absolute  number  of  vibrations  corre- 
sponding to  G_2,  G5  ? 

Art.  423.  147.  What  is  the  length  of  the  sonorous  wave  corre- 
sponding to  G  ,  G"2  ? 

Art.  428.  148.  What  is  the  relative  number  of  vibrations  corre- 
sponding to  F1?  F^,  G^,  G?  The  absolute  number? 

Art  429.  149.  In  the  key  of  A  what  notes  are  sharped? 

Art.  434.  150.  What  is  the  length  of  the  sonorous  wave  corre- 
sponding to  C2  when  made  in  carbonic  acid  gas?  (Compare  408.) 

OPTICS. 

Art.  441.  151.  It  is  calculated  that  the  light  from  the  polar  star 
requires  :\\  years  t<>  reach  the  earth;  what  is  its  distance? 

Art.  446.  152.  What  are  the  rehuive  intensities  <»f  two  lights  that 
cast  equal  shadows  at  distances  from  an  opaqur  rod  respectively  G 
inches  and  6  feet '! 


PROBLEMS   ON  PYROXOMICS.  457 

153.  A  wax  candle  is  fixed  at  10  inches  from  the  opaque  rod; 
what  must  be  the  distance  of  a  gas  light  from  the  same  rod  to  cast 
an  equal  shadow  when  the  gas  burns  with  "  12  candle  power'-? 

Art,  473.  154.  What  will  be  the  index  of  refraction  when  light 
from  crown  glass  into  bisulphide  of  carbon  ?    When  it  passes 
in  the  other  direction  ? 

Art.  495.  155.  What  will  be  the  relative  lengths  of  two  solar 
spectra  produced  under  the  same  circumstances  by  prisms  of  quartz 
and  of  bisulphide  of  carbon? 

Art.  506.  156.  With  red  taken  as  unity,  find  the  ratio  between 
the  relative  number  of  vibrations  in  the  colors  of  the  spectrum,  and 
compare  with  the  relative  number  of  sonorous  waves  in  an  octave. 
Will  the  comparison  warrant  any  analogy  between  vibrations  of  light 
and  of  sound? 

Art.  524.  157.  What  is  the  magnifying  power  of  a  lens  whose 
focal  length  is  T}7  of  an  inch? 

Art.  527.  158.  With  this  lens  as  an  objective  and  an  eye  piece  of 
5  inches  focal  length,  how  powerful  a  compound  microscope  can  be 
constructed  ? 

PYRONOMICS. 

Art.  552.  159.  Construct  a  table  showing  the  equivalence  between 
the  Fahrenheit  and  Centigrade  scales  for  every  10  degrees  between 
the  freezing  and  boiling  points  of  water. 

160.  Reduce  —  220°  F.  to  Centigrade.  Reduce  142°.65  F.  to  Cen- 
tigrade. Reduce  -f  273°  C.  to  F. 

Art.  554.  161.  What  is  the  linear  co-efficient  of  expansion  for 
iron?  For  steel?  For  brass? 

162.  What  is  the  ratio  between  the  two  last?  How  much  will  a 
railway  track  100  miles  long  expand  on  being  heated  from  0°  F.  to 
110°  F.? 

Art.  557.  163.  How  many  thermal  units  are  required  to  raise  1 
pound  of  water  from  0°  C.  to  1°  C. ?  One  kilogramme  of  water? 

164.  How  many  thermal  units  are  required  to  raise  80  pounds  of 
water  from  32°  F.  to  212°  F.  ?  Suppose  a  pound  of  coal,  if  econom- 
ically burned,  to  have  this  thermal  power;  how  many  pounds  of 
mercury  can  it  raise  from  —  37°.9F.  to  662°  F.?  How  many  pounds 
of  iron  would  it  raise  from  32°  F.  to  2132°  F.  ? 


458  NATURAL  PHILOSOPHY. 

Art.  561.  165.  How  many  pounds  of  lead  would  it  raise  from 
32°  F.  to  the  melting  point  of  lead  ? 

Art.  566.  166.  How  much  ice  at  32°  F.  will  the  same  fuel  melt? 

167.  How  many  thermal  units  will  be  evolved  by  the  freezing  of 
100  cubic  feet  of  water  ? 

168.  If  this  freezing  takes  place  in  a  cellar  containing  10000  cubic 
feet  of  air,   how  much  will  the  air  be  heated  if  all  the  effect  is 
expended  on  it? 

Art.  572.  169.  How  many  thermal  units  are  required  to  raise  10 
pounds  of  alcohol  from  32°  F.  to  its  boiling  point  ? 

Art.  574.  170.  What  is  the  altitude  of  a  station  at  which  water 
boils  at  180°  F.? 

Art.  579.  171.  How  many  thermal  units  are  required  to  evaporate 
10  pounds  of  boiling  alcohol  ? 

Art.  584.  172.  What  will  be  the  bulk  of  steam  formed  from  10 
pounds  of  water  at  212°  F.  ?  At  249°.5  F.  ?  At  306°  F.  ? 

Art.  588.  173.  How  much  faster  will  a  rod  of  copper  conduct  heat 
than  an  equal  rod  of  iron  ? 

Art.  619.  174.  How  many  pounds  of  ice  may  be  changed  to  steam 
by  the  burning  of  10  pounds  of  coal?  By  10  pounds  of  alcohol? 

Art.  624.  175.  What  is  the  mechanical  equivalent  of  the  heat 
produced  by  the  burning  of  1  pound  of  coal? 

176.  How  many  thermal  units  are  evolved  in  an  hour  by  a  stream 
of  water  with  a  section  1  foot  square  and  a  fall  of  60  feet? 

Art.  626.  177.  To  what  temperature  would  a  cannon  ball  moving 
at  the  rate  of  960  feet  per  second  be  raised  if  suddenly  stopped  ? 
How  many  thermal  units  would  be  evolved  if  the  ball  weighed  60 
pounds? 

Art.  637.  178.  What  is  the  efficiency  of  a  boiler  capable  of  evap- 
orating 10  cubic  feet  of  water  each  minute?  How  much  anthracite 
coal  will  be  required  in  au  hour? 


INDEX. 


THE    NUMBERS    REFER    TO    THE    PAGES. 


Aberration,  spherical  by  reflec- 
tion     256 

spherical  by  refraction  ...  267 

chromatic 272 

Absorption  of  gases 45 

of  light 246 

bands .    .    .    .  275 

of  heat 340 

Achromatism 272 

Achromatic  lenses 273 

Acoustics,  defined 214 

Acoustic  tubes 218 

Acoustic  properties  of  rooms  .    .  224 

Action  and  reaction 59 

diffused 62 

Adhesion 27 

compared  with  cohesion   .    .    28 
phenomena  connected  with    38 

recapitulation  of 50 

of  air  to  falling  liquids  ...  163 

Adjutage,  effect  of 163 

Affinity 27 

Air,  composition  of 172 

pressure  of 173 

properties  of 181 

pump,  Sprengel's 164 

Bunsen's 164 

Leslie's 179 

experiments  with     .    .    .181 

condenser 184 

gun 186 

chamber,  use  of 192 

when  saturated  with  moist- 
ure   321 

Ampere's  law 422 

theory  of  magnetism     ...  428 


Angle  of  incidence  and  reflec- 
tion      61,  209,  247 

visual 244 

optic 245 

of  refraction 257 

polarizing 301 

Annealing 36 

Archimedes,  principle  of    .    .    .148 

pi-oblem  of 158 

Artesian  wells U6 

Atmosphere,  pressure  of     ...  173 

illustrated 175 

height  of 186 

pressure  at  different  levels  .  187 
on  the  human  body  .  .  .189 
effect  on  boiling  point  .  322 

Atom,  defined 20 

Attraction,  capillary 41 

magnetic 364 

electrical 374 

explained 381 

Aurora     Borealis,     connection 

with  magnetic  storms  .    .  372 

described 399 

Aurora  tube 394 

Balance 82 

Ballistic  curve 113 

pendulum 127 

Balloons 184 

Barker's  mill 168 

Barometer,  mercurial 174 

aneroid 179 

heights  measured  by .    .    .    .188 

fluctuations  of 188 

as  a  weather  guide      ....  189 
4459) 


460 


NA  TURA L   PHIL  OSOP1I  \ '. 


Batteries,  magnetic 367 

electrical 388 

voltaic 407 

Beats,  musical 222 

Bodies,  classified 8 

immersed  in  fluids     .    .    .    .  147 

floating 149 

aeriform  classified 171 

sonorous 213 

transparency  of,  etc 238 

incandescent 239 

Body,  defined 7 

Boiling  points,  table  of    .    .    .    .322 
how  influenced  ......  322 

Breezes,  land  and  sea 315 

Brittleness 35 

Bunsen's  air  pump 164 

battery 411 

Buoyancy  of  liquids 147 

center  of 151 

Burning  glasses 262,  340 

Burton,  Spanish 91 

Camera  obscura 242 

photographer's 284 

draughtsman's 285 

Capillary  action 39 

Capstan 85 

Cartesian  diver 150 

Catoptrics 247 

Caustic  curve 256 

Cements 27 

Center  of  gravity 63 

of  suspension 118 

of  oscillation 121 

of  percussion 126 

Centrifugal  force 128 

Centripetal  force 128 

Chemical  physics,  defined  ...    12 
Chemical  sources  of  heat    ...  347 

of  electricity 401 

Chemical  effects  produced 

by  statical  electricity   .    .  395 
by  dynamical  electricity  .    .  416 

Chemistry,  defined 11 

Chords,  musical 230 

compound 231 

Chromatics -<i.s 

Circuit,  electrical W2 

simph-  ami  compound    ...  407 

telegraphic 4:jo 

Climate,   iutluenced  by  specific 

heat  ot  water :{10 


Climate,   influenced    by   latent 

heat  of  fusion     ....  318 
by  latent  heat  of  evapora- 
tion       330 

Clock,  pendulum  applied  to    .    .124 

how  regulated 123 

electric 435 

Clothing 335 

Clouds,  how  electrified     .    .    .    .397 

Coal,  value  in  thermal  units  .    .  348 

mechanical  equivalent  of .    .363 

Cog  wheels 86 

Cohesion 27 

how  estimated 29 

Cold,  sensation  of     ......  305 

produced   by   freezing   mix- 
tures   318 

by  evaporation      .....  329 

Collision  of  bodies 59 

destructive  effect,  of    ....    63 

Colors 268 

primary 269 

complementary 269 

wave  lengths  of 279 

how  determined 280 

natural,  of  bodies 280 

power    of    absorbing    solar 

heat 344 

Combustion 347 

Compass,  mariner's 370 

Compressibility 25 

Condensation   and   rarefaction, 

waves  of 205 

Condensation  of  aeriform  bodies  185 

Condenser  of  air 184 

electrical 387 

Conduction  of  sound 220 

of  heat 332 

estimated  by  touch  ...  333 

applications  of 334 

of  statical  electricity     .    .    .  375 

of  dynamical  electricity   .    .  406 

Construction,  method  by    ...    ."><) 

Convection  of  heat 336 

of  electricity 392 

Crane 98 

Crank 359 

Culinary  paradox 323 

Current,  electrical 402 

direction  of 403 

primary  and  induced     .    .    .436 

extra 437 

thermo-electric  .  .  442 


INDEX. 


461 


Daniell's  battery 411 

Dead  points 359 

Declination  of  the  needle  ...  370 
Dt-  la  Rive's  floating  battery  .  .  424 

Density 23 

Drw  point 321 

\h-\\-.  formation  of 343 

Dialysis 49 

Diamagnetic  substances  ....  368 

Diathermancy 341 

Diffraction 279 

Diffusion  of  liquids 46 

of  gases 47 

Dioptrics 257 

Direction,  line  of 66 

Discharge  of  liquids,  rate  of  .  .  162 

Discharging  rod 388 

Distances,  how  estimated  .  .  .  245 

of  lightning  estimated  ...  398 

Distillation 327 

Divisibility 19 

Ductility 35 

Dynamics,  denned 51 

considered 106 

Earth,  variation  of  gravity  on  .  116 
found  by  pendulum     .    .  120 

attraction  of 116 

curvature  of 116 

cause  of  present  form    .    .    .  132 
diurnal  revolution  proved    .  125 

magnetism  of 369 

Ebullition,  defined 319 

how  influenced 322 

Echo 223 

Elastic  bodies,  collision  of  ...    60 

Elasticity,  defined 29 

kinds  of,  classified     ....    30 

table  of 32 

Electricity 364 

defined 374 

statical  electricity 373 

law  of 375 

transmission  of     ....  375 

distribution  of 382 

quantity  and  intensity  of  383 
charge  by  cascade     ...  390 

phenomena  of 391 

kinds  of  discharge  of    .    .392 
points  and  flames     .    .    .  392 

effects  of 393 

recapitulation  of  .    .    .    .400 
atmospheric  electricity  .    .    .  397 


Electricity,  dynamical    .    .    .    .401 

current 402 

direction  of     ....  403 

energy  of 405 

quantity  of 405 

intensity  of     ....  406 
conductors  of  .    .    .    .406 

effects  of 412 

negative    plate,    how    pro- 
tected     404 

current  induction 421 

recapitulation 444 

thermo 441 

animal 443 

Electric  spark 393 

duration  and  velocity  of   .    .394 

light 414 

alarms 434 

clocks 435 

Electrical  induction 377 

apparatus 383 

battery 388 

pendulum 374 

hail 391 

pistol 396 

Electrodes 405 

Electrolysis 416 

Electrophorous 379 

Electroscope 376 

Electro-chemical  series,  table  of  417 

Electro-metallurgy 418 

Electro-motive  series,  table  of   .  404 

Electroplating 419 

Elect-retyping 420 

Electro-magnets 427 

Electro-magnetism 422 

Oersted's  discovery    .    ,    .    .  422 

Ampere 'slaw 422 

Electro-magnetic  rotation  ...  426 

machines 429 

Elements,  number  known  ...     8 

Engine,  fire 193 

steam 356 

electro-magnetic 429 

magneto-electrical     ....  438 
Equilateral  hyperbola     ....    40 

Equilibrium 68 

relation  of  solids  to  gravity  .    69 

of  liquids 144 

of  floating  bodies 151 

Evaporation,  laws  of 319 

cold  produced  by 329 

water  frozen  by 330 


462 


NATURAL   PHILOSOPHY. 


Kxchanges,  theory  of  heat      .    .  338 

Kxpansibility 25 

Expansion,  an  effect  of  heat .    .  305 

cubical  and  linear ;>OG 

unequal,  of  solids  .    .    .    .    .  307 
used  to  measure  heat     ...  308 

co-efficient  of 310 

force  in 311 

in  solidi  lying 317 

Extension 14 

Eye,  structure  of 285 

accommodation  of     ....  287 
shape  of 288 

Faraday's  theory  of  induction  .  380 

Far-sightedness 289 

Field  of  view  of  lenses    ....  290 

Fire  alarms,  electric 434 

Fire  engines 193 

Flame,  cause  of 273 

Flexibility 31 

Floating  bodies,  laws  of  .    .    .    .149 

Fluids,  defined 8 

manner  of  action 135 

transmission  of  pressure  in  .  136 

diathermancy  of 342 

Fluorescence 278 

Fly  wheel 359 

Foot  pound,  defined 74 

Force,  defined 7 

how  applied 29 

impulsive  and  continuous    .    51 
constant  and  variable   ...    52 

manner  of  action 54 

striking 62 

elastic,  of  gases 171 

of  expansion       311 

not  annihilated 355 

Forces,  classified 9 

resolution  of 57 

centripetal  and  centrifugal  .  128 

Foucault's  pendulum 125 

Franklin's  electrical  experiment  397 

Fraunhofer's  lines 271 

Freezing  point 316 

Feezing  mixtures 318 

Friction,  manner  of  action     .    .    27 

classified 101 

laws  of 101 

Fusion W 


Galvanism    .... 
Galvani's  experiment 


401 


Galvanometer 423 

Gamut 226 

Gases,  defined 8 

classified 172 

diathermancy  of 342 

Gassiot's  water  battery    .    .    .    .414 
Gauge  for  tension  of  aeriform 

bodies 177 

Geisler's  tubes 441 

Gravesande's  ring 306 

Gravitation,  terrestrial   »   ...    63 

universal 114 

recapitulation  of 116 

Gravity 64 

center  of 65 

how  found 65 

direction  of 64 

poi nt  of  application  of  .    .    .    65 

intensity  of 106 

Gravity,  specific,  defined    ...    23 

tables  of 24 

how  found 152 

Grove's  battery 410 

gas  battery 412 

Gyroscope 133 

Hardening 36 

Hardness 35 

Harmony  in  music 230 

Harmonics 234 

Hearing,  defined 212 

limits  of 218 

Heat,  defined 307 

effect  in  expansion     ....  305 

fusion 315 

vaporization 319 

incandescence 239 

distribution  of  by  conduction  332 

by  convection 336 

by  radiation 338 

dynamical  theory  of  .    .    .    .350 

reflection  of 339 

refraction  of 340 

absorption  of 340 

transmission  of 340 

sources  of 345 

solar,  estimated 346 

animal 347 

(.1  combustion,  estimated  .    .  348 

Heat  litfhtnini,' 398 

Meinlit  ol  the  ainn»-|.here  ...  187 
Heights  measured  by  tlu-  barom- 
eter     188 


INDEX. 


463 


Heights  measured  by  the  ther- 
mometer   

Helix 

Holtz's  electrical  machine  .  .  . 
Horse  power,  defined 

of  steam  boilers 

Hydraulics,  defined 

Hydraulic  press 

Hydraulic  ram 

Hydrodynamics,  defined  .  .  . 

considered 

Hydro-electric  machine .  .  .  . 
Hydrometers  of  constant  vol- 
ume   

of  constant  weight  .  .  .  . 

Hydrostatics 

Hydrostatic  bellows 


Images,  virtual 

real 

multiple 

formed  by  direct  light  .  .  . 
by  plane  mirrors  .... 
by  concave  mirrors  .  .  . 
by  convex  mirrors  .  .  . 
by  convex  lenses  .... 
by  concave  lenses  .  .  . 
by  mirrors  and  lenses,  re- 
capitulated   

in  the  eye 

Impenetrability 

Incandescence 

Inclination  of  the  needle    .    .    . 

Inclined  plane 

laws  of 

examples  of 

bodies  rolling  down   .... 

Indestructibility 

Induction,  of  magnetism    .    .    . 
of  statical  electricity  .... 
Faraday's  theory  of    .    .    .    .380 
essential   in   electrical   phe- 
nomena     381 

of  dynamical  electricity  .  .  421 
of  secondary  currents  .  .  .  436 
magneto-electrical  .  .  .  .4:37 

coils 439 

Inertia 18 

law  of 54 

Instruments,  musical 234 

Insulators 375 

.350 


It] 


Joule's  equivalent. 
N.  P.  30. 


Kaleidoscope 250 

Key,  signal 431 

Lantern,  magic 292 

Latent  heat 317 

table  of,  for  liquids     .    .    .    .  318 

of  vapors 328 

of  vapors,  applied 331 

effect  of  water  in  nature  318,  330 

Lenses,  classified 262 

convex,  foci  of 263 

axis  of 263 

secondary  axis 264 

formation  of  images  by  .  265 

concave,  foci  of 266 

formation  of  images  by  .  267 

magnifying 289 

illuminating  power  of     .  290 

crystalline 286 

Level  surface  defined 145 

spirit 146 

Levers 77 

illustrations  of 78 

bent 79 

compound 81 

applications  of 81 

Leyden  jar 387 

theory  of 388 

Light,  wave  theory  of 238 

sources  of 239 

velocity  of 240 

pencils  and  beams  of .    .    .    .241 

intensity  of 243 

compared  by  shadows      .  244 
disposition  of  incident  .    .    .246 

absorption  of 246 

reflection  of 247 

diffused 247 

intensity  of  reflected     ...  248 

refraction  of 2-57 

atmospheric  refraction  ...  259 

total  reflection 259 

refraction  by  regular  surfaces  261 

by  prisms 262 

by  lenses 262 

decomposition  of 268 

dispersion  of 271 

homogeneous 273 

properties  of 277 

interference  of 278 

length  of  waves 279 

double  refraction  of  ....  297 
polarized 298 


464 


NATURAL   PHILOSOPHY. 


Li-lit,  electric 414 

Lightning 398 

conductors 399 

Liquids,  defined 8 

compressible 135 

transmission  of  pressure  by  .  136 
effect  of  gravity  on    ....  138 

pressure  of 139 

in  motion 163 

equilibrium  of 144 

buoyancy  of 147 

in  motion 160 

range  of  flowing 161 

volume  discharged     .    .    .    .162 
velocity  of  discharge  .    .    .    .162 

waves  in 198 

as  conductors  of  heat     ...  333 

diathermancy  of 342 

as  conductors  of  electricity  .  406 
Liquefaction  of  vapors    ....  327 

Load,  defined 74 

Loadstone 364 

Luminous  tube 393 

Luminous  bodies 238 

Luminous  effects  of  statical  elec- 
tricity     393 

Machine,  defined 74 

advantages  of 76 

Machines,  simple 77 

compound 98 

recapitulated 100 

useful  effect  of 105 

for  water  power 166 

for  raising  water 190 

electrical 383 

magneto-electrical  ....  438 

Magnetism 364 

induction  of 366 

terrestrial 368 

source  of 373 

Ampere's  theory  of  .  .  .  .  428 

Ma-nets 364 

how  prepared 427 

When  saturated 428 

Magnetic  battery 367 

Magnetic  substances :;I;T 

Magnetic  force,  lines  of   .... 

Magnetic  elements 369 

changes  of ,T72 

Magnetic  poles,  terrestrial  .  .  .  :\i\'.t 

intensity 371 

to-electrical  induction  .  I.;: 


Magneto-electrical  machine    .    .  438 

Magic  lantern 292 

Magnitude 14 

Malleability 35 

Manometers 177 

Marcet's  globe 324 

Mariotte's  law 177 

Matter,  defined 7 

properties  of,  classified  .    .    .    11 

Mechanics 51 

Mechanism,  human 99 

Mechanical  equivalent  of  heat  .  350 

Medium,  for  sound 217 

for  light 238 

Melody 230 

Melting  points,  table  of  .    .    .    .316 

Meniscus 262 

Microphone 435,6 

Microscopes,  simple 289 

compound 293 

solar 292 

Mirage 260 

Mirrors 248 

formation  of  images  by  plane  249 

curved 251 

concave  spherical 251 

formation  of  image  of  lu- 
minous point     ....  251 
formation  of  images  by  .  253 

convex  spherical 255 

aberration  of  sphericity  of    .  250 

Mobility 17 

Molecules,  defined 7 

Molecular  forces 9 

energy  of 354 

Momentum 53 

Monochord 225 

Morse's  telegraph 431 

receiver    432 

alphabet 4&S 

Motion,  absolute  and  relative    .    17 

rate  of 17 

uniform  and  varied    ....    52 

Newton 'slaws  of 54 

simple  and  compound   .    .    .    55 

recapitulated 73 

impediments  to 100 

circular 128 

of  waves 1!I7 

Music,  the  pleasure  in 2:  ill 

major  and  minor  modes     .     .  12-'!1 

transposition  in •_':;:; 

Musical  sounds          .  .225 


INDEX. 


465 


Musical  rate  of  vibration  deter- 
mined     225 

absolute  number  of  vibra- 
tions in 228 

interval 228 

scales 229 

instruments 23-1 

Natural  philosophy,  defined  .    .    11 

Near-sightedness 288 

Needle,  magnetic ; 

astatic 

Newcomen's  engine 356 

Newton's  laws  of  motion  ...    54 

wheel 270 

rings 278 

telescope 296 

Nodes 200 

in  pipes 236 

Nodal  lines 202 

Octave  in  music 226 

Oersted's  discovery 422 

Opera  glass 296 

Optics 238 

Optic  nerve,  structure  of     ...  287 

Optical  instruments 284 

Oscillation,  center  of 121 

Osmose 48 

Parallel  motion 359 

Pascal's  experiment  on  pressure 

of  liquids 141 

with  barometer 173 

Pendulum 117 

employed  to  determine  grav- 
ity      120 

compound 121 

compensating 123 

applied  to  clocks 124 

Foucault's 125 

ballistic 127 

Penumbra 242 

Percussion,  center  of 126 

Phonograph,  Edison's 214 

Phosphorescence 239 

Physics,  defined 12 

Pitch  of  sound 215 

Pneumatics 172 

Pneumatic  paradox 19o 

Poles,  of  magnets 365 

magnetic,  of  earth      ....  369 
of  voltaic  element .    .  .405 


Polar  force,  defined 365 

Polarized  light,  explanation  of  .  299 
mused  by  double  refraction  .  298 

by  absorption 300 

by  reflection 301 

by  refraction 302 

rotatory 303 

applications  of 304 

Porosity 21 

Power,  defined 74 

Pressure,  transmission  of  in  liq- 
uids    136 

Problems 445 

Projectiles 112 

Pulley 89 

Pump,  lifting 191 

air 164,  179 

forcing 192 

Pyrometer 306 

Pyrheliometer 345 

Quantity  of  electricity  defined  .  383 

Radiant  heat,  disposition  of  .  .  339 
applications  of 344 

Radiation  of  light 241 

of  heat 338 

Rainbow,  formation  of  primary  281 
of  secondary 283 

Range  of  projectiles 112 

of  spouting  liquids  .  .  .  .161 

Reaction  in  hard  bodies  ....  58 
in  soft  bodies 62 

Reaction  wheels 168 

Receiver,  Morse's 432 

Reflection,  of  solids 61 

of  waves 209 

of  sound 222 

of  light 247 

total 259 

of  heat 339 

Refraction,  of  sound 224 

of  light 257 

index  of 258 

laws  of 259 

atmospheric 259 

by  regular  surfaces  .  .  .  261 

by  prisms 262 

by  lenses 262 

double 297 

of  heat 340 

Relay 433 

Resistance,  defined 64 


466 


NATURAL   PHILOSOPHY. 


Resistance  of  fluids 103 

Resolution  of  forces 57 

Refinance 1224 

Resonant  bodies 216 

Rest 17 

Retina,  duration  of  impression 

on 287 

Rigidity  of  cords 103 

Rivers,  velocity  of 165 

Ruhmkorfs  coil 440 

Safety,  position  of,  in  thunder 

storms 398 

Safety  valve 357 

Scale,  chromatic .    .  232 

diatonic 226 

natural,  in  music 233 

thermometric 309 

Screw 96 

law  of 96 

differential 97 

applications  of 98 

endless 98 

Shadows 241 

used  to  measure  intensity  of 

light 244 

Sight»  to  what  due 287 

Siphon 193 

Size  of  objects,  how  estimated    .  245 

Smee's  battery 409 

Soft  ruing  of  steel 3fi 

Solenoid 424 

Solution 42 

Solvent powers 43 

Sound,  deflued 212,  214 

conditions  requisite  for     .    .  213 

quality  of 214 

intensity  of 215 

distance  of  audibility    .    .    .218 

velocity  of 219 

co-existence  <>f 221 

combination    and    interfer- 
ence of 222 

reflection  of -222 

refraction  of 224 

Sounds,  musical 225 

laws  of L'_7 

rate  determined 22S 

Speaking  trumpet 219 

Specific  heat :;i.; 

how  a>c.-rt  ained 313 

tables  of 314 

effect  of,  in  nature 315 


Specific  gravity,  defined.    ...    23 

tables  of 24 

standard  of 152 

how  ascertained 152 

for  heavy  solids    ....  153 

for  light  sol  ids 154 

for  soluble  solids  ....  154 

for  liquids 154 

for  gases 158 

practical  applications  of   .    .158 

Spectrum,  solar 269 

dark  lines  in 271 

explanation  of 276 

reversed 276 

properties  of 277 

Spectrum  analysis 273 

Spheroidal  state 325 

Spirit  level 146 

Statics,  defined 51 

considered 74 

Statics  and  dynamics,  general    .    51 

Stability  of  solids 70 

applications  of 72 

of  floating  bodies 152 

Steam,  mechanical  power  of  .    .362 

temperature  of 324 

superheated 325 

Steam  engine 356 

Steam  boilers 362 

Steel,  how  tempered 37 

how  magnetized 427 

Steelyard 81 

Strength,  ultimate  and  proof .    .    31 
on  what  dependent    ....    32 

Strength  of  materials 31 

Stereoscope 291 

Sublimation 319 

Tables,  of  weights 16 

velocities 18 

specific  gravity 24 

units  of  pressure 26 

direction  of  strain 29 

ultimate  strength 32 

elasticity 32 

hardness  of  minerals  ...  35 
relative  malleability,  etc.  .  .  36 

solubility  of  uases 44 

absorption  of  gases  ....  45 
co-efficients  of  friction  .  .  .  103 
friction  of  wagons  on  roads  .  103 
useful  i-H'ert  of  machines  .  .  105 
atmospheric  pressure  ...  187 


INDEX. 


467 


Tables,  of  velocity  of  sound  .  .  22u 
indices  of  refraction  ....  258 
wave  lengths  of  colors  .  .  .279 
expansion  by  heat  ....  311 

specific  heat 314 

melting  points 316 

latent  heat  of  liquids     .    .    .318 

boiling  points 322 

at  different  pressures   .    .  324 

at  different  levels      .    .    .324 

latent  heat  of  vapors     ...  329 

volume  of  different  vapors  .  331 

thermal  conductivity     ...  333 

reflecting  powers 339 

diathermancy  of  solids      .    .  341 

of  liquids 342 

of  gases 342 

radiating,  reflecting,  and  ab- 
sorbent powers 343 

heat  of  combustion  ....  348 
secular  magnetic  changes  .  372 
conductors  and  insulators  .  375 

electrics   . 376 

electro-motive  series ....  404 
powers  of  current  conduction  406 
electro-chemical  series  .  .  .417 

Telegraph,  electric 430 

Wheatstone's 431 

Morse's 431 

House's  and  Hughes 's    ...  435 

Telescope 293 

astronomical 294 

terrestrial 295 

Galileo's 295 

reflecting 296 

Herschel's 296 

Newton's 296 

equatorial 294 

Tempering 37 

Temperature 308 

Tenacity,  defined 31 

how  increased 34 

Tension  of  aeriform  bodies     .    .  171 

how  ascertained 176 

Thermo-electricity 411 

Thermo-multiplier 442  | 

Thermometer 308  ' 

Thermal  unit 313 

Throttle  valve 360 

Thunder 398 

Tone,  musical 215  ! 

major  and  minor 230 

semitone 230  i 


Torricelli,  theorem  of 161 

barometer 173 

Tourmaline  pincette 300 

Transposition  in  music    ....  233 
Turbines 168 

Umbra 241 

Undulations 196 

formation  of 197 

progressive 198 

of  solids 198 

of  liquids,  surface 198 

stationary 199 

progressive  changed  to  sta- 
tionary       200 

in  fluids 202 

in  aeriform  bodies      ....  205 

of  light 278 

Units  of  weight  and  measure     .    15 

pressure 26 

velocity  and  time 52 

thermal 313 

Vapors,  defined 171 

Vaporization 319 

Velocity,  defined 17,  52 

table  of 18 

of  uniformly  varied  motion    53 
of  falling  bodies     .    .  *.    .    .106 

increment  of 109 

laws  of 110 

of  bodies  thrown  upward  .    .112 

of  liquids 161 

Vena  contracta 163 

Vesicular  condition 45 

Vibrations,  of  pendulums  .    .    .118 

of  cords 198 

simple  and  complete  ....  199 

of  elastic  solids 201 

simultaneous 211 

recapitulation 212 

sympathetic 217 

of  sonorous  cords 225 

absolute  rate  of 228 

of  light 238 

Vision,  to  what  due 287 

limits  of  distinct 288 

anomalies  of 289 

Voltaic  element,  simple  ....  401 

batteries 407 

arc 415 

Voltameter 417 

Volume 14 


468 


NATURAL  PHILOSOPHY. 


Warmth,  sensation  of     ....  305 

Water,  expansion  of 312 

specific  gravity 152 

a  standard  for  temperature  .  308 

specific  heat 313 

latent  heat 317 

effect  on  climate     .    .    .   315,  318 

evaporation  of 320 

tables  of  boiling  points  of     .  324 
frozen  by  its  own  evapora- 
tion    330 

Water  power 166 

Water  wheels 166 

Watt's  steam  engine 358 

Wave  motion  described  ....  197 

surface  of  fluids 198 

combination    and    interfer- 
ence of 203 

Waves,  of  the  sea 204 

of  condensation  and  rarefac- 
tion    205 

velocity  of 208 

intensity  of 208 

combination    and   inter- 
ference of 208 

reflection  of 209 


Waves,    co-existence    of    sono- 
rous     ±21 

length  of  sonorous      ....  228 
length  of  luminous     .    .    .    .279 

Wedge,  law  of 95 

applications  of 95 

Weight,  absolute 15 

specific "23 

Weighing,  modes  of 81 

method  of  double 84 

Wheatstone's  telegraph  .    .    .    .431 

Wheel  and  axle 84 

law  of 85 

differential 86 

WlK-rls,  train  of 86 

how  connected 88 

water 106 

Wilde's  magneto-electrical  ma- 
chine       439 

Windlass 85 

Winds 337 

Winter's  electrical  machine    .    .383 

Work,  defined 74 

how  calculated 75 

relation  between,  and  heat  .  350 
interior 353 


ECLECTIC  EDUCATIONAL  SERIES. 

Published  by  VAN  ANTWERP,  BRAGG  &  CO.,  Cincinnati  and  New  York. 

ECLECTIC  MANUAL  OF  METHODS 
FOR  THE  ASSISTANCE  OF  TEACHERS. 

How  to  teach  Language.  How  to  teach  Grammar. 

How  to  teach  Composition.  How  to  teach    Geography. 

How  to  teach   Reading.  How  to  teach  History. 

How  to  teach  Arithmetic.  How  to  teach  Penmanship. 

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This  Manual  is  the  outgrowth  of  numerous  requests  from  young  and 
inexperienced  teachers  of  country  schools  in  nearly  every  part  of  the 
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During  the  past  few  years  there  has  been  a  strenuous  effort  made 
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the  chaos  in  which  the  ungraded  schools  have  heretofore  existed. 
Superintendents  have  held  meetings,  and  discussed  methods  and  the 
proper  use  of  text-books  ;  they  have  also,  in  many  cases,  issued  manu- 
als to  their  teachers,  setting  forth  the  results  of  the  conferences,  and 
making  many  valuable  suggestions  as  to  the  future  conduct  of  the 
schools.  These  manuals,  although  frequently  differing  in  unessential 
details,  agree  in  recommending  a  definite  and  uniform  course  of 
study,  and,  as  far  as  practicable,  a  uniformity  of  text-books  in  classes. 

Wherever  these  suggestions  of  the  superintendents  have  been  fol- 
lowed, the  schools,  without  exception,  have  been  improved  in  char- 
acter. But  many  difficulties  confront  the  inexperienced  teacher, 
regarding  which  he  receives  no  aid  from  the  Superintendents'  Manual. 
Not  the  least  of  these,  perhaps,  is  owing  to  the  fact  that  he  does  not 
understand  how  to  use  his  text-books  to  the  best  advantage. 

It  has  been  the  endeavor  to  show,  in  the  Eclectic  Manual,  what 
the  method  is  for  each  subject,  and  how  it  should  be  applied. 

Bound  in  full  cloth ;  262  pages. 

Single  specimen  copy  for  examination  with  a  view  to  first 
introduction,  60  cents. 

"  The  Eclectic  Manual  is  a  safe  and  reliable  guide  for  the  teacher, 
whether  in  the  graded  or  ungraded  school."— J.  M.  GREENWOOD, 
Supt.  ScJiools,  Kansas  City. 

"  I  have  examined  the  Eclectic  Manual  of  Methods  and  think  it 
well  adapted  to  secure  the  results  aimed  at." — H.  K.  EDSON,  Ch.  of 
Didactics,  Iowa  College. 

"I  congratulate  you  on  the  Eclectic  Manual  of  Methods.  It  ought 
to  have  a  wide  sale,  and  will  doubtless  be  of  vast  benefit  to  all  classes 
of  teachers,  but  especially  to  those  who  struggle  against  the  heavy 
odds  of  unclassified  schools."— H.  C.  SPEEK,  late  State  Supt.  Kansas. 


Eclectic    Educational  Series. 

Duffefs  New  French  Method, 

BY  F.  BUFFET,  PARIS,  FRANCE. 
Revised  by  ALFRED  HENNEQUIN,  A.  M.,  University  of  Michigan. 

12mo.,  cloth,  394  pp. 
From  the  Preface  : 

THIS  revised  edition  of  Professor  Buffet's  FRENCH  METHOD  does  not 
differ  in  the  main  from  the  original  work,  which  lias,  in  a  very  short 
time,  become  so  favorably  known  in  Europe  and  in  this  country.  It  is 
still  an  eminently  "Progressive  and  Practical  Method  for  the  Study 
of  the  French  Language." 

The  object  to  be  obtained  in  studying  a  foreign  language  is  certainly 
to  understand  it,  to  speak  it,  and  to  write  it  at  the  earliest  possible 
moment.  With  this  in  view,  Professor  Buffet  introduces  the  student 
to  the  language  itself  in  its  most  useful  and  practical  forms  from  the 
very  beginning.  It  is,  in  fact,  a  colloquial  grammar,  simple,  but 
thorough,  short,  and  complete. 

We  do  not  claim,  as  reviser,  to  have  added  much  to  the  intrinsic 
value  of  the  work.  Our  object  has  been  to  adapt  the  book  to  the  re- 
quirements of  American  schools  and  colleges.  Most  of  the  important 
changes  that  have  been  made  occur  in  Part  First,  in  which  have  been 
introduced  numerous  tables  and  diagrams,  explaining  the  parts  of 
speech  in  a  more  systematic  form  than  Professor  Buffet  had  attempted. 
Short  rules  have  also  been  given  where  deemed  advisable,  and  many 
of  the  original  rules  have  been  re-worded. 

PART  SECOND  has  called  for  very  few  changes  aside  from  the  intro- 
duction of  Tables  and  Biagrams.  The  order  of  the  Rules  of  Syntax 
has  been  maintained. 

The  verbs  have  also  been  left  in  the  order  given  by  Professor  Buffet, 
and  the  same  classification  retained.  We  have,  however,  given  an 
enlarged  formation  of  the  tenses,  adding  numerous  references  to  the 
same,  thereby  doing  away,  to  a  very  great  extent,  with  the  mechani- 
cal memorizing  of  the  irregular  verbs.  Various  other  minor  changes 
have  also  been  made  in  the  verbs,  mostly  through  the  introduction  of 
Tables  and  Biagrams. 
University  of  Michigan,  Ann  Arbor.  ALFREB  HENNEQUIN. 


KEY  TO  DUFFETS  FRENCH  METHOD. 
Duffei*  s  French  Literature, 

Brief  Extracts  in  Prose  and   Poetry  from  the   writings  of  Fifty  of  the 
best  French  writers.      I2mo.,  cloth,  168  pp. 

PUBLISHED    BY 

VAN  ANTWERP,  BRAGG  &  CO.,  Cincinnati  and  New  York. 


ECLECTIC  EDUCATIONAL  SERIES. 

Published  by  VAN  ANTWERP,  BRAGG  &  CO.,  Cincinnati  and  New  York. 

ENGLISH  LANGUAGE. 

HARVEY'S  LANGUAGE  COURSE. 

By  THOMAS  W.  HARVEY,  A.  M. 

HARVEY'S  REVISED  ELEMENTARY  GRAMMAR   AND 

COMPOSITION.  I2mo.,  cloth,  160  pp. 

HARVEY'S  REVISED  ENGLISH    GRAMMAR,   larno.,   half 

roan,  264  pp. 

A  practical  course  in  Oral  and  Written  Language  Lessons,  Com- 
position and  English  Grammar.  The  Golden  Mean  between  the  too 
labored  attempt  at  simplification,  and  thescientific  technical  gram- 
mar. 

HOLBROOK'S  NORMAL  SERIES. 

By  A.  HOLBROOK,  Principal  National  Normal  University. 

HOLBROOK'S  TRAINING  LESSONS,  lamo.,  135  pp. 
HOLBROOK'S  COMPLETE  ENGLISH  GRAMMAR,  I2mo., 
cloth,  204  pp. 

PINNEO'S  GUIDE  TO  COMPOSITION 

A  Series  of  Practical  Lessons  designed  to  simplify  the  Art  of  Writing  Composition, 
By  T.  S.  PINNEO,  A.  M.,  M.  D.  i2mo,  cloth,  162  pp.  Designed  for  those  who  desire 
a  concise  but  comprehensive  course  of  Instruction  in  Composition. 

PINNEO'S  EXERCISES  IN  FALSE  SYNTAX. 

izmo.,  104  pp.  Systematically  arranged  ;  contains,  also,  promiscuous  examples  of 
correct  and  incorrect  syntax. 

PINNEO'S    EXERCISES  IN    PARSING   AND    ANALYSIS. 

i2mo.,  120  pp.  A  brief  review  of  the  leading  principles  of  Grammar,  conveniently 
arranged  for  reference ;  followed  by  a  well-arranged  series  of  selections  from  the  besl 
authors,  with  explanatory  notes  and  references. 

WILLIAMS'S  PARSER'S  MANUAL. 

The  Parser's  Manual,  embracing  classified  examples  in  nearly  every  variety  of 
English  construction.  By  JOHN  WILLIAMS,  A.  M.  izmo.,  cloth,  264  pp. 

OBJECT  LESSONS  AND  COMPOSITION. 

Things  Taught :  Systematic  Instruction  in  Composition  and  Object  Lessons.  By 
Dr.  M.  E.  LILIENTHAL  and  ROBT.  ALLYN,  M.  A.  Prepared  by  order  of  the  Cin- 
cinnati School  Board.  i6mo.,  96  pp. 

LANGUAGE  EXERCISES. 

For  Primary  Classses.  By  J.  MICKLEBOROUGH,  Prin.  Cincinnati  Normal  School, 
and  C.  C.  LONG,  Prin.  2oth  District  School,  Cincinnati. 

PART  I.     For  First  and  Second  Reader  classes,  i2mo.,  48  pp. 

Part  II.     For  Third  and  Fourth  Reader  classes,  12010- ,  96  pp 

TEACHER'S  EDITION,  i2mo.,  187  pp.  Contains  Parts  I  and  II  ;  Course  of  Study  in 
Language  Lessons  for  Cincinnati  Schools ;  plans  for  developing  the  Exercises  and 
methods  for  presenting  them;  and  much  valuable  information  and  many  suggestive 
hints  for  the  successful  teaching  of  Language. 

These  Exercises  follow  the  Language  Course  lately  adopted  by  the  Cincinnati  Peda- 
gogical Association. 


ECLECTIC  EDUCATIONAL  SERIES. 

VAN  ANTWERP,  BRAGG  &  CO.,  Publishers,  Cincinnati  and  New  York. 

NORTON'S  CHEMISTRY. 

THE  ELEMENTS  OF  CHEMISTRY. 

BY  SIDNEY  A.  NORTON,   A.M.,  M.  D. 
I2mo,  cloth,  504  pages. 

The  present  edition  has  been  thoroughly  revised  and  has  also  been 
enlarged  by  the  introduction  of  a  dozen  chapters  treating  of  OKC.AMC 
CHEMISTRY. 

This  work  is  intended  as  a  text-book,  not  as  a  manual  for  reference. 
The  author  has  endeavored  to  select  such  chemical  phenomena  as 
represent  the  cardinal  principles  of  the  science,  giving  preference  to 
those  which  are  easily  reproduced  by  the  student,  and  which  enter 
into  the  affairs  of  common  life.  To  attain  this  end,  he  has  omitted 
many  excellent  experiments  which  require  the  use  of  expensive 
apparatus,  and  has  substituted  others  which,  if  less  "  classical,"  are 
of  easier  application. 

The  engravings  represent  well-fashioned  apparatus;  but  no  one 
ought  to  be  deterred  from  attempting  an  experiment  because  he  has  not 
the  exact  shaped  figure.  Any  drug-store  or  kitchen  will  afford  bottles 
and  tumblers,  which  may  be  used  in  place  of  flasks  and  beakers.  In 
some  way,  the  experiments  ought  to  be  tried. 

As  regards  nomenclature,  the  author  has  endeavored  to  follow  as 
closely  as  possible,  in  a  work  of  this  size,  the  rules  of  the  London 
Chemical  Society.  Old  and  well-known  names  have  been  retained 
because  of  their  common  use. 

As  regards  notation,  it  must  be  born  in  mind  that  all  formula" 
are  alike  subject  to  change.  No  greater  mistake  can  be  made  than 
that  any  formula  (except  a  binary)  tells  the  whole  truth  about  a 
molecule,  or  that  any  formula  which  correctly  represents  the  percent- 
age composition  of  a  substance  may  not  be,  at  times,  available  in 
fixing  in  the  mind  of  the  student  the  fact  to  be  remembered.  The 
author  has,  therefore,  used  the  formula  that  appeared  convenient  at 
the  time  ;  and  feels  that  an  experience  of  twenty  years'  teaching  war- 
rants him  in  advising  his  fellow-teachers  hot  to  attempt  to  place  theory 
above  practice.  The  use  of  theory  is  to  enable  one  to  generalize  known 
facts  and  predict  new  ones  ;  the  business  of  teaching  is  to  enable  the 
student  to  master  facts,  principles,  and  laws  already  ascertained  and 
established. 

By  the  same  Author: 

Norton's    Natural   Philosophy. 
Norton's  Elements  of  Physics. 


ECLECTIC  EDUCATIONAL  SERIES. 

VAN  ANTWERP,  BRAGG  &  CO.,  Publishers,  Cincinnati  and  New  York. 

SCIENCE. 

ECLECTIC  PHYSIOLOGY  AND  HYGIENE. 

Accurately  illustrated.  Special  attention  given  to  effects  of  Narcotics 
and  Stimulants,  discussion  of  habits  leading  to  pain  and  disease,  proper 
sanitary  conditions,  etc.  Price,  60  c.  ;  postage  and  mailing,  10  c. 

NORTON'S  PHYSICS. 

Elements  of  Physics  for  Academies  and  Common  Schools.  By 
S.  A.  NORTON,  A.  M.,  Prof,  in  Ohio  Agricultural  and  Mechanical 
College.  I2mo,  cloth,  286pp.  Price,  80  c.  ;  postage  and  mailing,  13  c. 

NORTON'S  NATURAL  PHILOSOPHY. 

The  Elements  of  Natural  Philosophy.  By  S.  A.  NORTON,  A.  M. 
A  new  treatise,  embracing  latest  discoveries  to  date  of  publication. 
I2mo,  cloth,  458  pp.  Price,  $1.10;  postage  and  mailing,  18  c. 

NORTON'S  CHEMISTRY. 

The  Elements  of  Chemistry.  By  S.  A.  NORTON,  A.  M.  I2mo,  cloth, 
504  pp.  Illustrated.  New  Edition,  including  Organic  Chemistry.  Price, 
$1.10;  postage  and  mailing,  i8c. 

ANDREWS'S   ELEMENTARY  GEOLOGY. 

An  Elementary  Geology,  designed  especially  for  the  Interior  States. 
By  E.  B.  ANDREWS,  LL.  D.,  late  of  the  Ohio  Geological  Corps,  and 
Professor  in  Marietta  College.  I2mo,  cloth,  269  pp.  and  Index.  432 
Illustrations.  Price,  $1.00;  postage  and  mailing,  I7c. 

GREGORY'S  POLITICAL   ECONOMY. 

A  new  Political  Economy,  by  JOHN  M.  GREGORY,  LL.  D.,  Ex-Pres. 
Illinois  Industrial  University.  Contains  many  features  of  striking 
originality.  I2mo,  clo.,  394pp.  Price,  $1.20;  postage  and  mailing,  20  c. 

SCHUYLER'S   LOGIC. 

The  principles  of  Logic.  By  A.  SCHUYLER,  LL.  D.,  Pres't  of  Bald- 
win University;  author  of  Algebra,  Trigonometry,  Surveying,  etc. 
I2mo,  cloth,  1 68  pp.  Price,  60  c. ;  postage  and  mailing,  loc. 

ANDREWS'S   CONSTITUTION. 

Manual  of  the  Constitution  of  the  United  States.  Designed  for  the 
instruction  of  American  youth  in  the  duties,  obligations,  and  rights  of 
citizenship.  By  ISRAEL  WARD  ANDREWS,  D.  D.,  Ex-President  Mari- 
etta College.  I2mo,  cloth,  408  pp.,  with  Index  and  Appendices,  em- 
bracing important  state  papers.  Price,  $1.00;  postage  and  mailing,  17  c. 

"  In  each  aspect  of  its  usefulness,  the  work  can  not  fail  to  meet  with  approval, 
and,  as  a  text-book,  it  is  by  all  odds  the  best  of  its  kind."— THE  NATION. 

GOW'S  MORALS  AND  MANNERS. 

Good  Morals  and  Gentle  Manners.  A  systematic  text-book  on  Moral 
and  Social  Law.  By  ALEX.  M.  Gow,  A.  M.  I2mo,  cloth  252  pp. 
Price,  $1.00;  postage  and  mailing,  i;c. 


ECLECTIC  EDUCATIONAL  SERIES. 

Published  by  VAN  ANTWERP,  BRAGG  &  CO.,  Cincinnati  and  New  York. 

COMPOSITION,  RHETORIC,  LITERATURE. 

ECLECTIC  LANGUAGE   LESSONS. 

Uy  M.  E.  THALHKFMER.  For  Primary  Classes.  Designed  to  accus- 
tom children  to  a  correct  use  of  the  elementary  forms  of  speech,  with 
as  little  reference  as  possible  to  the  technicalities  of  grammar.  Pro- 
fusely Illustrated.  Bound  in  Full  Cloth,  I2mo,  no  pp.  Price  35  c. ; 
postage  and  mailing  6  c. 

HARVEY'S   REVISED    ELEMENTARY   GRAMMAR    AND 
COMPOSITION. 

Lessons  in  grammar,  sentence-making  and  composition.  Ideas  are 
first  developed  by  intelligent  questioning  and  appropriate  illustrations; 
then,  clothed  in  words. 

Sentence-making  and  Composition  are  presented  in  a  natural  and  at- 
tractive manner;  and  both  teacher  and  pupil  are  aided  by  well  executed 
and  appropriate  pictorial  illustrations. 

I2mo,  cloth,  160  pp.      Price  42  c. ;   postage  and  mailing  7  c. 
HEPBURN'S  RHETORIC. 

Manual  of  English  Rhetoric,  by  A.  D.  HEPBURN,  Davidson  College, 
N.  C.  The  principles  and  rules  of  pure  English  Rhetoric  stated 
briefly  and  exemplified.  Adapted  to  instruction  by  sections  or  by 
topics.  I2mo,  310  pp.  Price,  $1.00;  postage  and  mailing,  17  c. 

"  Hepburn's  Rhetoric  has  the  merits  of  being  thorough,  orderly,  and  fresh 
in  its  treatment  of  the  subject,  as  well  as  clear  and  pure  in  style." — PROF. 
MOSES  COIT  TYLER,  Univy  of  Mich. 

PINNEO'S  GUIDE  TO  COMPOSITION. 

Improved  Edition.     250  carefully  graded  lessons,  designed  to  simplify 
the  art  of  writing  Composition.     Also,  full  instructions  on  the  use  of 
capital  letters,  punctuation  marks,  etc.      By  T.  S.  PINNKO,  A.  M.,  M.  I). 
I2mo,  cloth,  162  pp.      Price,  60  c;   postage  and  mailing,  IOC. 
SMITH'S  STUDIES  IN  ENGLISH  LITERATURE. 

I2mo,  cloth,  427  pp.  Illustrated.  Studies  in  English  Literature, 
including  Selections  from  the  Five  Great  Classics, — Chaucer,  Spenser, 
Shakespeare,  Bacon,  and  Milton, — and  a  History  of  English  Litera- 
ture from  the  Earliest  times  to  the  death  of  Dryclen  in  1700.  By  M. 
\Y.  SMITH,  A.  M.,  Hughes  High  School,  Cincinnati,  O.  Price,  $1.20; 
postage  and  mailing,  20  c. 
PINNEO'S  EXERCISES  IN  FALSE  SYNTAX. 

Systematically  arranged  ;  also,  promiscuous  examples  of  correct  and 
incorrect  syntax.  I2mo,  104  pp.  Price,  35  c. ;  postage  and  mailing,  6  c. 
PINNEO'S  EXERCISES  IN  PARSING  AND  ANALYSIS. 

A  brief  review  of  the  leading  principles  of  Grammar,  conveniently 
arranged  for  reference;  followed  by  a  well-arranged  series  of  selections 
from  the  best  authors,  with  explanatory  notes  and  references.      I2mo, 
1 2O  pp.      Price,  40  c.  ;  postage  and  mailing,  7  c. 
WILLIAMS'S  PARSER'S  MANUAL. 

Embracing  classified  examples  in  nearly  every  variety  of  English 
Construction.  By  JOHN  \Yn.i.i.\Ms,  A  M.  121110,  cloth,  264  pp.  Price, 
65  c. ;  postage  and  mailing,  i  i  •  . 


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Published  by  VAN  ANTWERP,  BRAGG  &  CO.,  Cincinnati  and  New  York. 

THALHEIMER'S  HISTORICAL  SERIES. 

I>v  M.  K.  THALHKIMKR,  Teacher  of  History  and  Composition  in 
Packer  Collegiate  Institute.  For  Graded  Schools,  High  Schools, 
Academies,  and  Colleges.  These  books  furnish  to  teachers,  stu- 
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Ancient  and  Modern  History. 

ECLECTIC  HISTORY  OF  THE  UNITED   STATES. 

i2mo,  half  roan,  392  pp.  Copiously  illustrated  with  Maps,  Portraits,  etc. 
Contains  reliable  References  and  Explanatory  Notes  ;  Declaration  of  Indepen- 
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THALHEIMER'S  HISTORY  OF  ENGLAND. 

i2mo,  288  pp.  A  compact  volume,  comprehensive  in  scope,  but  sufficiently 
brief  to  be  completed  in  one  school  term.  Its  statements  of  historical  facts  are 
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THALHEIMER'S   GENERAL   HISTORY.     (AVr/W.) 

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schools,  and  those  of  higher  grade  unable  to  give  much  time  to  the  study  of 
history,  are  here  exactly  met.  The  teacher  is  aided  by  Review  Questions  at 
the  end  of  each  principal  division  of  the  book,  and  by  references  to  other  works 
in  which  each  subject  will  be  found  more  fully  treated.  Price,  $1.20;  postage 
and  mailing,  20  c. 

THALHEIMER'S  ANCIENT  HISTORY. 

A  Manual  of  Ancient  History  from  the  Earliest  Times  to  the  fall  of  the 
Western  Empire,  A.  D.  476.  8vo.,  full  cloth,  365  pp.,  with  Pronouncing  Vo- 
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ANCIENT  HISTORY  in  three  Parts  has  been  published,  riz  : 

1.  Thalheimer's  History  of  Early  Eastern  Monarchies. 

2.  Thalheimer's  History  of  Greece. 

3.  Thalheimer's   History  of  Rome. 

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THALHEIMER'S  MEDIAEVAL  AND  MODERN  HISTORY. 

A  Manual  of  Mediaeval  and  Modern  History.  8vo.,  cloth  uniform  with 
Thalheimer's  Ancient  History.  455  pp.,  and  very  full  Index.  Numerous 
double-page  Maps.  A  sketch  of  fourteen  centuries,  from  the  fall  of  one  empire 
at  Ravenna  to  the  establishment  of  another  at  Berlin.  Price,  $1.60;  postage 
and  mailing,  27  c. 

ECLECTIC  PRIMARY  HISTORY 

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Profusely  illustrated  with  superior  engravings  and  portraits.  Square  121110, 
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MAILMAN'S  HISTORY  OF  PEDAGOGY. 

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MAILMAN'S  KINDERGARTEN   CULTURE. 

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CHAPTERS  ON  SCHOOL  SUPERVISION!  A  Practical  Treatise  on  Superintendence; 
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HOW  TO  TEACH. 

A  Manual  of  Methods  for  a  Graded  Course  of  Instruction  ;  embracing  the  sub- 
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THE  SCIENCE  OF  EDUCATION.     I2mo,  234  pp.,  cloth. 
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By  JOHN  OGDEN,  A.  M.,  Principal  Ohio  Central  Normal.  Designed  to  present 
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RITTER'S  GEOGRAPHICAL  STUDIES.     I2mo,  356  pp. 
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Re-publication  of  two  important  works  of  the  Great  Geographer,  CARL  RITTER, 
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DOERNER'S  TREASURY  OF  GENERAL  KNOWLEDGE. 

Part  I.  205  pp.,  half  roan.      Price,  50  cents  ;  postage  and  mailing,  10  cents. 

Part  II.  291  pp.,  half  roan.      Price,  65  cents  ;  postage  and  mailing,  10  cents. 
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THE  ECLECTIC  QUESTION  BOOK  AND  TEACHER'S 

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I'.y  ALEXANDER  DCNCAN,  A.  M.  (Questions  for  Complete  Review  of  Spelling, 
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SMART'S      MANUAL      OF      FREE     GYMNASTICS     AND 
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A  conci  •  .  pr:i<  ti<  al  Trratisc,  designed  for  use  in  the  school  room.  Illustrated. 
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KRUST'S   LIFE  OF  PESTALOZZI. 

//i,  His  Life,  Work,  and  Influence  :  By  HERMAN  K R rsi,  A .  M.,  Instructor 
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